# What is Heat capacities: Definition and 28 Discussions

Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
Heat capacity is an extensive property. The corresponding intensive property is the specific heat capacity, found by dividing the heat capacity of an object by its mass. Dividing the heat capacity by the amount of substance in moles yields its molar heat capacity. The volumetric heat capacity measures the heat capacity per volume. In architecture and civil engineering, the heat capacity of a building is often referred to as its thermal mass .

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1. ### I Cannot understand formula for molar heat capacities of an ideal gas

Homework Statement:: I am trying to understand a formula given in our book for determining molar heat capacity of an ideal gas under different thermodynamic processes using a single formula, but it is confusing. The exact formula for different processes is in the screenshots below. Can someone...
2. ### Heat capacity vs Thermal conductivity in a LN2 bath

I worked on a lab experiment that was meant to measure heat capacity but left me with some other questions. The students measured the mass of a cup of liquid nitrogen as it boiled off, recording mass vs time. Then they drop a solid object into the bath, one experiment with a small bit iron...
3. ### What is the molar heat capacity of an ideal gas at constant pressure and volume?

Homework Statement 117 J of energy is supplied as heat to 2.00 moles of an ideal gas at constant pressure, the temperature rises by 2.00 K. Calculate the molar heat capacity at constant pressure C_p,m and the molar heat capacity at constant volume C_v,m for the gas. Is the gas monatomic or...
4. ### Relation between heat capacities and van der Waals equation

Homework Statement Find the expression for c_p - c_v for a van-der-waals gas, with the equation of state \Bigg{(}p+\dfrac{a}{V^2}\Bigg{)}(V-b)=RT Homework EquationsThe Attempt at a Solution Basically I've proved c_p - c_v = \Bigg{[} p + \Bigg{(}\dfrac{\partial E}{\partial V}\Bigg{)}_T...
5. ### Specified equation of state from heat capacity

Homework Statement The constant-volume heat capacity of a particular simple system is c_v = AT^3 where A is a constant. In addition the equation of state is known to be of the form (v-v_0)p = B(T) where B(T) is an unspecified function of T. Evaluate the permissible functional form of B(T)...
6. ### How can heat capacity be determined when both pressure and volume are changing?

Hello all, I am taking a thermodynamics course and unfortunately my professor is not very instructive. I have attended every class and I still feel lost. I was wondering how it is possible to find heat capacity if both the pressure and the volume are changing? I was under the impression that...
7. ### Change in entropy of a resistor

Homework Statement Consider a thermally insulated resistor with resistance R=20 Ω and mass m=5.0 g. The resistor is made of a material with specific heat capacity c=850 J/(g-K) and carries a current of 2.0 A for a time period of 1.0 s. a) Calculate the increase in the temperature of the...
8. ### Calculation confirmation needed -- energy stored in heated water

Hi Guys I'm new the PF and hope I'm posting I the correct place, apologies to admin if not ;-). I'm working on a project at home and maths is not my strong suit. I have an equation that I need to complete and involves converting thermal heat capacity in water into electric power. From what I...
9. ### I Understanding the Definition of Cp and its Relationship to Cv: Explained

Hi all, I'm working through a derivation of the general relationship between Cp and Cv and there's one point which is confusing me. I understand that and and that this implies the following: but isn't this equal to 0? Shouldn't the two partial derivatives on the right...
10. ### Heat Capacities Given Equation of State

Homework Statement Given the equation of state ##V(P,T)=V_1\cdot exp(\frac{T}{T_1}-\frac{P}{P_1})## where ##V_1\;,T_1\;,P_1## are constants: a. derive an equivalent equation ##P(V,T)##; b. given ##C_V=DT^3## where D is a const, calculate the entropy of the system ##s(V,T)## up to a const; c...
11. ### Water anomaly -- Heat capacities

From relation C_p-C_v=[P+(\frac{\partial U}{\partial V})_T](\frac{\partial V}{\partial T})_P In case of water ##(\frac{\partial V}{\partial T})_P<0## so ##C_p<C_v##? Right?
12. ### Heat capacity of water -- experimental determination

Homework Statement A quantity of water in a beaker of negligible thermal capacity is cooled to a few degrees below freezing point. The beaker is then placed in a warm room, and the times recorded at which it is at various temperatures as it gradually warms. The observations were...
13. ### Specific heat Capacities of metals

Hi Admin, please allow me to post this here: The General Formula for Specific Heat Capacity is: C(Total) = C(electron)+C(phonon) C(electron) = aT where a is the sommerfield constant. C(phonon) = bT^3 this time i don't know what is b (some constant) so my problem is, how can i determine b...
14. ### Specific Heat Capacities in co-ordination with Thermodynamics

Please help me qualitatively in the following points : 1) If in a system(consider a cylinder) fixed with a piston , if the piston is moved suddenly then how can a process be adiabatic. 2) I understood that the process would be irreversible but, if the process is adiabatic then is the relation...
15. ### Find molar mass and number of degrees of freedom from heat capacities.

Hey having a bit of trouble with this one. I really don't know how to start. Think I just simply don't have the right equations or I'm using the wrong units. Hopefully you guys can help me. Homework Statement Find the molar mass and the number of degrees of freedom of molecules in a gas with...
16. ### Heat capacities and negative temperature

Hi everybody, I have the following doubt. We know that for a thermodynamic system the following equality holds: $$C_P-C_V=-T\frac{\left[\left(\frac{\partial P}{\partial T}\right)_V\right]^2}{\left(\frac{\partial P}{\partial V}\right)_T}$$ Now, the mechanical stability of the system...
17. ### What do the symbols H and U represent in thermodynamics equations?

Can someone please tell me what does the symbol H and what does the symbol U represent in these equations: http://www.taftan.com/thermodynamics/CP.HTM"][/PLAIN] http://www.taftan.com/thermodynamics/CP.HTM
18. ### Thermodynamics Question (entropy and heat capacities)

Homework Statement Two somewhat related problems: 1. Using the expression for change in entropy of an ideal gas per mole: ΔS=CV+R ln(V) Calculate the change in entropy, change in Helmholtz Free Energy and change in Gibbs Free Energy when 1 mole of an ideal gas is compressed from 1 atm to 20...
19. M

### Heat capacities, adiabatic processes, etc

I am confused why the heat capacity at constant pressure can be different from the heat capacity at constant volume. I am also having difficulties absorbing the material regarding the kinetic theory of gases, such as keeping all the ΔE_int changes with what processes etc. Why can adiabatic...
20. ### Heat capacities of ideal gases

Homework Statement A cylinder contains 0.2mol of Helium at 30 degrees C and is heated different ways. How much heat is needed to raise the temperature to 70C while keeping thevolume constant? Homework Equations dQ=dU+dT nCpdT=nCvdT+nRdT The Attempt at a Solution What I am...
21. ### Why Do Heat Capacities Use Derivatives of Entropy in Their Formulas?

Hi all, I'm working with the heat capacities definition and I have got a confusion. I don't understand why we can express them like Cp = T(∂S/∂T)p Cv = T(∂S/∂T)v I know that Cp=(dQ/dT)p = (∂H/∂T)p with H equal to TdS + VdP and Cv=(dQ/dT)v = (∂U/∂T)v with U equal to TdS + PdV, My...
22. ### Thermodynamic derivation involving heat capacities

I have the answer to this question but I'm finding it hard making sense of it... Q5) Dervive a relationship relating Cp-Cv to the isothermal compressibility (∂p/∂V)T and the coefficient of thermal expansion (∂V/∂T)p. Hint: consider the intensive entropy S as a function of T and V. So I've...
23. ### Experiment: Ratio of the principal specific heat capacities of air

Homework Statement To find the ratio of the specific heat capacities of air (γ). Homework Equations PVγ=constant The Attempt at a Solution I performed the experiment a number of times to get an average for γ The experiment consisted of a container with release valve, a hand...
24. ### Heat capacities of a gas mixture.

Homework Statement 1 gram of Hydrogen H_2 and 1 gram of Helium He are put together into a container of 10 L in volume and at a temperature of 27°C. (a) Find the pressure (b) Find the molar specific heat capacities C_v and C_p, as well as \gamma = \frac{C_p}{C_v} of this gas mixture...
25. ### Molar specific heat capacities for gases

For an isochoric process, dV = 0 therefore dW=0 So from 1st of Thermodynamics, dQ = dU + 0 or, n*Cp*dT = n*Cv*dT (Cp and Cv denote molar heat capacities of the gas at const pressure and volume resp.) therefore we get Cp = Cv .(how can this be possible once we know Cp - Cv = R ?)
26. ### Calculating the ratio between heat capacities of a gas

Hi, my task is to calculate the ratio (gamma) between the specific heats of a gas (Cp and Cv). The only information I have is a table of data for the pressures and volumes of the gas at different temperatures. I don't know if its monatomic, diatomic etc. (it's a later task to determine this)...
27. ### Molar Heat Capacities and Specific Heats for Ideal Gases

Homework Statement a. Consider an ideal gas being heated at constant volume, and let Cv be the gas's molar heat capacity at constant volume. If the gas's infinitesimal change in temperature is dT, find the infinitesimal change in internal energy dU of n moles of gas. Express the...
28. ### Heat Capacities and Derivatives of Fugacity with Volume per Particle

Homework Statement This question refers to Pathria's Statistical Mechanics textbook. In this problem, there is the equation: \frac{C_P}{C_V} = \frac{\left(\partial z /\partial T \right)_P}{\left(\partial z /\partial T\right)_{\nu}} where z is the fugacity and \nu is the volume per...