What Do You Need to Know for Calculating Heat Capacity
Estrus Chapters
The heat capacity measures the amount of heat necessary to heighten the temperature of an object or system by one degree Celsius.
Learning Objectives
Explain the enthalpy in a system with abiding volume and pressure level
Key Takeaways
Key Points
- Heat capacity is the measurable physical quantity that characterizes the amount of heat required to change a substance'due south temperature by a given corporeality. Information technology is measured in joules per Kelvin and given past.
- The heat capacity is an extensive holding, scaling with the size of the arrangement.
- The oestrus capacity of most systems is not constant (though it can often be treated as such). It depends on the temperature, pressure, and volume of the organisation under consideration.
Key Terms
- heat chapters: The amount of oestrus free energy needed to raise the temperature of an object or unit of measurement of thing past one degree Celsius; in units of joules per kelvin (J/G).
- enthalpy: the full amount of energy in a arrangement, including both the internal energy and the energy needed to displace its environment
Heat Chapters
Heat capacity (usually denoted past a uppercase C, often with subscripts), or thermal capacity, is the measurable physical quantity that characterizes the corporeality of estrus required to alter a substance'due south temperature past a given amount. In SI units, rut capacity is expressed in units of joules per kelvin (J/G).
An object's heat capacity (symbol C) is defined as the ratio of the amount of rut energy transferred to an object to the resulting increase in temperature of the object.
[latex]\displaystyle{\text{C}=\frac{\text{Q}}{ \Delta \text{T}}.} [/latex]
Heat capacity is an all-encompassing property, and then it scales with the size of the system. A sample containing twice the corporeality of substance equally some other sample requires the transfer of twice as much heat (Q) to attain the same change in temperature (ΔT). For instance, if it takes 1,000 J to heat a block of iron, information technology would take two,000 J to heat a second block of iron with twice the mass as the first.
The Measurement of Heat Capacity
The heat capacity of most systems is not a constant. Rather, it depends on the state variables of the thermodynamic system nether study. In particular, it is dependent on temperature itself, also as on the pressure and the book of the organization, and the ways in which pressures and volumes have been allowed to alter while the arrangement has passed from i temperature to another. The reason for this is that pressure-volume work done to the arrangement raises its temperature by a mechanism other than heating, while pressure-volume work done by the system absorbs heat without raising the system'southward temperature. (The temperature dependence is why the definition a calorie is formally the energy needed to heat ane g of water from 14.5 to 15.v °C instead of generally by 1 °C. )
Different measurements of heat chapters can therefore be performed, almost commonly at abiding pressure and abiding volume. The values thus measured are usually subscripted (past p and V, respectively) to point the definition. Gases and liquids are typically also measured at constant volume. Measurements under constant force per unit area produce larger values than those at constant volume considering the constant force per unit area values also include heat energy that is used to practice work to expand the substance against the constant pressure as its temperature increases. This divergence is specially notable in gases where values under constant pressure are typically 30% to 66.vii% greater than those at abiding volume.
Thermodynamic Relations and Definition of Heat Capacity
The internal energy of a closed system changes either by adding rut to the organisation or by the arrangement performing work. Recalling the commencement constabulary of thermodynamics,
[latex]\text{dU}=\delta \text{Q}-\delta \text{W}[/latex].
For work as a result of an increment of the system volume we may write,
[latex]\text{dU}=\delta \text{Q}-\text{PdV}[/latex].
If the oestrus is added at constant book, then the second term of this relation vanishes and one readily obtains
[latex]\displaystyle{\left( \frac{\partial \text{U}}{\partial \text{T}}\right) _{\text{V}}=\left( \frac{\fractional \text{Q}}{\partial \text{T}}\correct) _{\text{V}}=\text{C}_{\text{Five}}}[/latex].
This defines the heat chapters at constant volume, C V. Another useful quantity is the heat capacity at constant pressure, C P. With the enthalpy of the organization given past
[latex]\text{H}=\text{U}+\text{PV}[/latex],
our equation for dU changes to
[latex]\text{dH}=\delta \text{Q}+\text{VdP}[/latex],
and therefore, at constant pressure, we accept
[latex](\frac{\partial \text{H}}{\partial \text{T}})_{\text{P}}=(\frac{\partial \text{Q}}{\partial \text{T}})_{\text{P}}=\text{C}_{\text{P}}[/latex].
Specific Heat
The specific rut is an intensive property that describes how much heat must be added to a item substance to heighten its temperature.
Learning Objectives
Summarize the quantitative relationship between estrus transfer and temperature change
Key Takeaways
Key Points
- Unlike the total estrus capacity, the specific heat capacity is independent of mass or volume. It describes how much rut must be added to a unit of measurement of mass of a given substance to raise its temperature by 1 degree Celsius. The units of specific rut capacity are J/(kg °C) or equivalently J/(kg K).
- The rut chapters and the specific heat are related by C=cm or c=C/m.
- The mass grand, specific estrus c, change in temperature ΔT, and heat added (or subtracted) Q are related by the equation: Q=mcΔT.
- Values of specific heat are dependent on the properties and phase of a given substance. Since they cannot be calculated easily, they are empirically measured and available for reference in tables.
Central Terms
- specific heat capacity: The amount of heat that must be added (or removed) from a unit mass of a substance to change its temperature past one degree Celsius. It is an intensive belongings.
Specific Heat
The heat capacity is an all-encompassing belongings that describes how much heat energy information technology takes to raise the temperature of a given system. However, information technology would exist pretty inconvenient to measure the heat capacity of every unit of matter. What we want is an intensive property that depends only on the blazon and phase of a substance and can be applied to systems of capricious size. This quantity is known equally the specific heat capacity (or only, the specific heat), which is the heat capacity per unit of measurement mass of a textile. Experiments show that the transferred heat depends on three factors: (1) The change in temperature, (ii) the mass of the system, and (3) the substance and phase of the substance. The last ii factors are encapsulated in the value of the specific heat.
Heat Transfer and Specific Heat Capacity: The rut Q transferred to cause a temperature change depends on the magnitude of the temperature change, the mass of the system, and the substance and phase involved. (a) The corporeality of heat transferred is directly proportional to the temperature change. To double the temperature change of a mass m, you lot need to add together twice the estrus. (b) The amount of heat transferred is also directly proportional to the mass. To cause an equivalent temperature change in a doubled mass, you lot need to add twice the oestrus. (c) The corporeality of oestrus transferred depends on the substance and its stage. If it takes an corporeality Q of heat to cause a temperature change ΔT in a given mass of copper, it will take 10.viii times that amount of rut to cause the equivalent temperature change in the same mass of water bold no phase change in either substance.
The dependence on temperature change and mass are easily understood. Because the (boilerplate) kinetic energy of an atom or molecule is proportional to the absolute temperature, the internal free energy of a system is proportional to the absolute temperature and the number of atoms or molecules. Since the transferred rut is equal to the change in the internal energy, the heat is proportional to the mass of the substance and the temperature change. The transferred rut also depends on the substance and so that, for example, the rut necessary to enhance the temperature is less for booze than for water. For the same substance, the transferred heat also depends on the stage (gas, liquid, or solid).
The quantitative relationship between estrus transfer and temperature change contains all three factors:
[latex]\text{Q}=\text{mc}\Delta \text{T}[/latex],
where Q is the symbol for estrus transfer, m is the mass of the substance, and ΔT is the alter in temperature. The symbol c stands for specific heat and depends on the cloth and phase.
The specific oestrus is the corporeality of estrus necessary to modify the temperature of 1.00 kg of mass by 1.00ºC. The specific heat c is a property of the substance; its SI unit is J/(kg⋅K) or J/(kg⋅C). Remember that the temperature change (ΔT) is the same in units of kelvin and degrees Celsius. Note that the full heat capacity C is simply the product of the specific heat chapters c and the mass of the substance k, i.due east.,
[latex]\text{C}=\text{mc}[/latex] or [latex]\text{c}=\frac{\text{C}}{\text{m}}=\frac{\text{C}}{\rho \text{V}}[/latex],
where ϱ is the density of the substance and 5 is its book.
Values of specific oestrus must mostly be looked up in tables, because there is no unproblematic way to calculate them. Instead, they are measured empirically. In full general, the specific oestrus also depends on the temperature. The tabular array below lists representative values of specific rut for various substances. Except for gases, the temperature and volume dependence of the specific heat of nigh substances is weak. The specific oestrus of water is v times that of drinking glass and ten times that of fe, which means that information technology takes five times as much heat to enhance the temperature of h2o the same corporeality every bit for drinking glass and ten times as much oestrus to enhance the temperature of h2o as for atomic number 26. In fact, h2o has one of the largest specific heats of any material, which is of import for sustaining life on Earth.
Specific Heats: Listed are the specific heats of diverse substances. These values are identical in units of cal/(thou⋅C).three. cv at abiding volume and at 20.0ºC, except as noted, and at ane.00 atm average pressure. Values in parentheses are cp at a constant pressure of i.00 atm.
Calorimetry
Calorimetry is the measurement of the estrus of chemical reactions or physical changes.
Learning Objectives
Clarify the relationship between the gas abiding for an ideal gas yield and volume
Key Takeaways
Key Points
- A calorimeter is used to measure the heat generated (or absorbed) by a physical change or chemical reaction. The science of measuring these changes is known every bit calorimetry.
- In order to practice calorimetry, information technology is crucial to know the specific heats of the substances existence measured.
- Calorimetry tin can be performed under constant volume or abiding pressure. The blazon of adding done depends on the conditions of the experiment.
Key Terms
- constant-pressure calorimeter: An instrument used to measure the heat generated during changes that exercise not involve changes in pressure.
- calorimeter: An apparatus for measuring the heat generated or absorbed by either a chemic reaction, change of phase or another physical alter.
- abiding-volume calorimeter: An musical instrument used to mensurate the heat generated during changes that do not involve changes in book.
Calorimetry
Overview
Calorimetry is the science of measuring the heat of chemic reactions or physical changes. Calorimetry is performed with a calorimeter. A simple calorimeter but consists of a thermometer attached to a metal container full of water suspended above a combustion chamber. The word calorimetry is derived from the Latin word calor, meaning heat. Scottish doctor and scientist Joseph Black, who was the start to recognize the distinction betwixt rut and temperature, is said to be the founder of calorimetry.
Calorimetry requires that the textile existence heated have known thermal properties, i.e. specific rut capacities. The classical dominion, recognized by Clausius and past Kelvin, is that the pressure level exerted past the calorimetric material is fully and rapidly determined solely by its temperature and volume; this rule is for changes that do not involve phase modify, such every bit melting of ice. There are many materials that do not comply with this dominion, and for them, more than complex equations are required than those beneath.
Water ice Calorimeter: The globe'south kickoff ice-calorimeter, used in the wintertime of 1782-83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the estrus evolved in variouschemical changes; calculations which were based on Joseph Black's prior discovery of latent heat. These experiments marker the foundation of thermochemistry.
Basic Calorimetry at Constant Value
Constant-volume calorimetry is calorimetry performed at a constant book. This involves the use of a constant-book calorimeter (one type is chosen a Bomb calorimeter). For constant-volume calorimetry:
[latex]\delta \text{Q}=\text{C}_{\text{V}}\Delta \text{T}=\text{mc}_{\text{V}}\Delta \text{T}[/latex]
where δQ is the increase of heat gained by the sample, CV is the heat capacity at constant volume, cv is the specific heat at constant volume, and ΔT is the change in temperature.
Measuring Enthalpy Change
To find the enthalpy change per mass (or per mole) of a substance A in a reaction between ii substances A and B, the substances are added to a calorimeter and the initial and concluding temperatures (before the reaction started and after it has finished) are noted. Multiplying the temperature modify past the mass and specific rut capacities of the substances gives a value for the energy given off or captivated during the reaction:
[latex]\delta \text{Q}=\Delta \text{T}(\text{thousand}_{\text{A}}\text{c}_{\text{A}}+\text{chiliad}_{\text{B}}\text{c}_{\text{B}})[/latex]
Dividing the energy alter by how many grams (or moles) of A were nowadays gives its enthalpy change of reaction. This method is used primarily in bookish teaching as it describes the theory of calorimetry. It does not account for the estrus loss through the container or the estrus chapters of the thermometer and container itself. In addition, the object placed inside the calorimeter shows that the objects transferred their heat to the calorimeter and into the liquid, and the rut captivated by the calorimeter and the liquid is equal to the heat given off by the metals.
Constant-Pressure Calorimetry
A abiding-force per unit area calorimeter measures the change in enthalpy of a reaction occurring in solution during which the atmospheric pressure remains constant. An example is a coffee-cup calorimeter, which is constructed from ii nested Styrofoam cups and a lid with ii holes, assuasive insertion of a thermometer and a stirring rod. The inner cup holds a known amount of a solute, ordinarily water, that absorbs the rut from the reaction. When the reaction occurs, the outer cup provides insulation. Then
[latex]\text{C}_{\text{P}}=\frac{\text{Westward}\Delta \text{H}}{\text{Thou}\Delta \text{T}}[/latex]
where Cp is the specific heat at abiding pressure, ΔH is the enthalpy of the solution, ΔT is the modify in temperature, W is the mass of the solute, and M is the molecular mass of the solute. The measurement of oestrus using a simple calorimeter, like the coffee cup calorimeter, is an example of constant-pressure calorimetry, since the pressure (atmospheric force per unit area) remains constant during the process. Abiding-force per unit area calorimetry is used in determining the changes in enthalpy occurring in solution. Under these weather the change in enthalpy equals the rut (Q=ΔH).
Specific Estrus for an Ideal Gas at Constant Force per unit area and Volume
An platonic gas has different specific heat capacities under constant volume or constant force per unit area conditions.
Learning Objectives
Explain how to derive the adiabatic alphabetize
Fundamental Takeaways
Key Points
- The specific heat at constant volume for a gas is given as [latex](\frac{\partial \text{U}}{\partial \text{T}})_{\text{V}}=\text{c}_{\text{v}}[/latex].
- The specific heat at constant pressure for an platonic gas is given as [latex](\frac{\partial \text{H}}{\partial \text{T}})_{\text{V}}=\text{c}_{\text{p}}=\text{c}_{\text{5}}+\text{R}[/latex].
- The rut capacity ratio (or adiabatic index ) is the ratio of the rut chapters at constant pressure to rut capacity at constant volume.
Key Terms
- Cardinal Thermodynamic Relation: In thermodynamics, the fundamental thermodynamic relation expresses an infinitesimal modify in internal energy in terms of minute changes in entropy, and volume for a closed system in thermal equilibrium in the following fashion: dU=TdS-PdV. Hither, U is internal free energy, T is absolute temperature, S is entropy, P is pressure and Five is volume.
- adiabatic index: The ratio of the heat capacity at constant pressure to heat capacity at constant book.
- specific estrus: The ratio of the amount of heat needed to raise the temperature of a unit mass of substance by a unit degree to the amount of heat needed to heighten that of the same mass of water past the aforementioned corporeality.
Specific Heat for an Platonic Gas at Constant Pressure and Volume
The heat chapters at constant volume of nR = 1 J·Thousand−1 of any gas, including an ideal gas is:
[latex](\frac{\partial \text{U}}{\partial \text{T}})_{\text{Five}}=\text{c}_{\text{v}}[/latex]
This represents the dimensionless oestrus chapters at constant volume; information technology is generally a function of temperature due to intermolecular forces. For moderate temperatures, the constant for a monoatomic gas is cv=3/2 while for a diatomic gas it is cv=five/2 (see ). Macroscopic measurements on heat capacity provide information on the microscopic construction of the molecules.
Molecular internal vibrations: When a gas is heated, translational kientic energy of molecules in the gas will increase. In addition, molecules in the gas may pick up many characteristic internal vibrations. Potential energy stored in these internal degrees of freedom contributes to specific heat of the gas.
The heat chapters at constant force per unit area of one J·K−i ideal gas is:
[latex](\frac{\partial \text{H}}{\partial \text{T}})_{\text{5}}=\text{c}_{\text{p}}=\text{c}_{\text{v}}+\text{R}[/latex]
where H=U+pV is the enthalpy of the gas.
Measuring the heat capacity at constant volume tin exist prohibitively difficult for liquids and solids. That is, pocket-size temperature changes typically require large pressures to maintain a liquid or solid at constant volume (this implies the containing vessel must be most rigid or at to the lowest degree very strong). Information technology is easier to measure the rut capacity at abiding pressure level (allowing the material to aggrandize or contract freely) and solve for the heat capacity at constant volume using mathematical relationships derived from the basic thermodynamic laws.
Utilizing the Cardinal Thermodynamic Relation nosotros can prove:
[latex]\text{C}_{\text{p}}-\text{C}_{\text{V}}=\text{T}(\frac{\fractional \text{P}}{\partial \text{T}})_{\text{V},\text{Due north}}(\frac{\partial \text{V}}{\partial \text{T}})_{\text{p},\text{North}}[/latex]
where the partial derivatives are taken at: constant volume and constant number of particles, and at constant pressure and constant number of particles, respectively.
The heat capacity ratio or adiabatic alphabetize is the ratio of the heat capacity at abiding pressure to oestrus capacity at constant volume. Information technology is sometimes also known as the isentropic expansion cistron:
[latex]\gamma =\frac{\text{C}_{\text{P}}}{\text{C}_{\text{V}}}=\frac{\text{c}_{\text{p}}}{\text{c}_{\text{v}}}[/latex]
For an ideal gas, evaluating the partial derivatives above according to the equation of land, where R is the gas constant for an platonic gas yields:
[latex]\text{pV} = \text{RT}[/latex]
[latex]\text{C}_{\text{p}}-\text{C}_{\text{V}}=\text{T}(\frac{\fractional \text{P}}{\fractional \text{T}})_{\text{5}}(\frac{\partial \text{Five}}{\fractional \text{T}})_{\text{p}}[/latex]
[latex]\text{C}_{\text{p}}-\text{C}_{\text{V}}=-\text{T}(\frac{\partial \text{P}}{\partial \text{Five}})_{\text{5}}(\frac{\partial \text{Five}}{\partial \text{T}})_{\text{p}}^{2}[/latex]
[latex]\text{P}=\frac{\text{RT}}{\text{V}}\text{northward} \to (\frac{\partial \text{P}}{\partial \text{5}})_{\text{T}}=\frac{-\text{RT}}{\text{V}^{2}}=\frac{-\text{P}}{\text{V}}[/latex]
[latex]\text{V}=\frac{\text{RT}}{\text{P}}\text{n} \to (\frac{\partial \text{V}}{\fractional \text{T}})^{ii}_{\text{p}}=\frac{\text{R}^{two}}{\text{P}^{two}}[/latex]
substituting:
[latex]-\text{T}(\frac{\partial \text{P}}{\fractional \text{5}})_{\text{5}}(\frac{\partial \text{V}}{\partial \text{T}})_{\text{p}}^{2}=-\text{T}\frac{-\text{P}}{\text{V}}\frac{\text{R}^{two}}{\text{P}^{2}}=\text{R}[/latex]
This equation reduces only to what is known as Mayer'southward relation:
Julius Robert Mayer: Julius Robert von Mayer (November 25, 1814 – March 20, 1878), a German physician and physicist, was ane of the founders of thermodynamics. He is best known for his 1841 enunciation of one of the original statements of the conservation of energy (or what is now known as one of the start versions of the first law of thermodynamics): "Energy can be neither created nor destroyed. " In 1842, Mayer described the vital chemical procedure now referred to as oxidation every bit the master source of energy for whatsoever living creature. His achievements were overlooked and credit for the discovery of the mechanical equivalent of heat was attributed to James Joule in the following year. von Mayer besides proposed that plants convert calorie-free into chemical energy.
[latex]\text{C}_{\text{P}}-\text{C}_{\text{V}}=\text{R}[/latex].
It is a simple equation relating the estrus capacities under abiding temperature and under constant pressure.
Solving Bug with Calorimetry
Calorimetry is used to measure the amount of heat produced or consumed in a chemic reaction.
Learning Objectives
Explain a bomb calorimeter is used to measure out oestrus evolved in a combustion reaction
Key Takeaways
Key Points
- Calorimetry is used to mensurate amounts of heat transferred to or from a substance.
- A calorimeter is a device used to measure the corporeality of rut involved in a chemical or concrete process.
- This means that the amount of oestrus produced or consumed in the reaction equals the amount of heat absorbed or lost by the solution.
Primal Terms
- heat of reaction: The enthalpy change in a chemical reaction; the amount of rut that a systems gives upwardly to its surroundings then information technology tin return to its initial temperature.
- combustion: A process where two chemicals are combined to produce heat.
Calorimeters are designed to minimize energy exchange between the system being studied and its environment. They range from simple coffee cup calorimeters used by introductory chemical science students to sophisticated bomb calorimeters used to determine the free energy content of nutrient.
Calorimetry is used to measure amounts of heat transferred to or from a substance. To do then, the heat is exchanged with a calibrated object (calorimeter). The change in temperature of the measuring part of the calorimeter is converted into the amount of rut (since the previous scale was used to institute its heat capacity ). The measurement of heat transfer using this arroyo requires the definition of a system (the substance or substances undergoing the chemical or physical alter) and its surroundings (the other components of the measurement appliance that serve to either provide heat to the system or absorb estrus from the system). Knowledge of the heat chapters of the surround, and conscientious measurements of the masses of the system and surroundings and their temperatures before and afterwards the process allows one to calculate the heat transferred as described in this section.
A calorimeter is a device used to measure the amount of heat involved in a chemical or concrete process. For example, when an exothermic reaction occurs in solution in a calorimeter, the estrus produced by the reaction is captivated by the solution, which increases its temperature. When an endothermic reaction occurs, the oestrus required is absorbed from the thermal energy of the solution, which decreases its temperature. The temperature change, along with the specific rut and mass of the solution, can then be used to summate the amount of rut involved in either example.
Coffee-Loving cup Calorimeters
Full general chemistry students often use uncomplicated calorimeters constructed from polystyrene cups. These easy-to-use "java cup" calorimeters permit more heat exchange with their surroundings, and therefore produce less accurate free energy values.
Construction of the Constant Volume (or "Flop") Calorimeter
Flop Calorimeter: This is the picture of a typical setup of bomb calorimeter.
A different type of calorimeter that operates at constant volume, colloquially known as a bomb calorimeter, is used to mensurate the energy produced by reactions that yield big amounts of heat and gaseous products, such equally combustion reactions. (The term "bomb" comes from the observation that these reactions tin can exist vigorous enough to resemble explosions that would damage other calorimeters.) This type of calorimeter consists of a robust steel container (the "bomb") that contains the reactants and is itself submerged in water. The sample is placed in the bomb, which is then filled with oxygen at high pressure level. A modest electric spark is used to ignite the sample. The free energy produced by the reaction is trapped in the steel bomb and the surrounding water. The temperature increase is measured and, along with the known estrus capacity of the calorimeter, is used to calculate the energy produced by the reaction. Bomb calorimeters require calibration to determine the heat chapters of the calorimeter and ensure accurate results. The scale is accomplished using a reaction with a known q, such as a measured quantity of benzoic acrid ignited by a spark from a nickel fuse wire that is weighed before and subsequently the reaction. The temperature change produced by the known reaction is used to determine the heat capacity of the calorimeter. The scale is generally performed each time before the calorimeter is used to gather research data.
Instance: Identifying a Metallic by Measuring Specific Heat
A 59.7 1000 slice of metal that had been submerged in boiling water was quickly transferred into 60.0 mL of water initially at 22.0 °C. The final temperature is 28.5 °C. Employ these data to determine the specific oestrus of the metal. Utilize this result to place the metal.
Solution
Bold perfect oestrus transfer, the heat given off by metal is the negative of the estrus taken in by water, or:
[latex]\text{q}_{\text{metal}}=-\text{q}_{\text{water}}[/latex]
In expanded grade, this is:
[latex]\text{c}_{\text{metal}} \times \text{m}_{\text{metallic}} \times \left( \text{T}_{\text{f,metal}}-\text{T}_{\text{i,metal}} \right) = \text{c}_{\text{water}} \times \text{m}_{\text{water}} \times \left( \text{T}_{\text{f,water}}-\text{T}_{\text{i,water}} \right)[/latex]
Noting that since the metal was submerged in humid water, its initial temperature was 100.0 °C; and that for water, 60.0 mL = 60.0 g; we have:
[latex]\left( \text{c}_{\text{metallic}} \right)\left( 59.7\text{ g} \right)\left( 28.5^{\text{o}} \text{C} - 100.0^{\text{o}} \text{C} \right) = \left( 4.18 \text{ J/g}^{\text{o}} \text{C} \correct) \left( 60.0\text{ g} \right)\left( 28.5^{\text{o}} \text{C} - 22.0^{\text{o}} \text{C} \right)[/latex]
Solving this:
[latex]\text{c}_{\text{metal}} = \dfrac{- \left( 4.184 \text{ J/g}^{\text{o}} \text{C} \correct) \left( sixty.0\text{ g} \right)\left( half-dozen.5^{\text{o}} \text{C} \correct)}{\left( 59.vii\text{ g} \correct)\left( -71.five^{\text{o}} \text{C} \right)} = 0.38 \text{ J/thou}^{\text{o}} \text{C} [/latex]
Our experimental specific heat is closest to the value for copper (0.39 J/1000 °C), so we identify the metal every bit copper.
Source: https://courses.lumenlearning.com/boundless-physics/chapter/specific-heat/
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