# What is Heat capacity: Definition and 437 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 Questions about my Understanding of Thermodynamics and Statistical Mechanics

Good afternoon all, I have two questions to check my understanding/understand better those questions. Why is heat capacity an important quantity in thermodynamics and statistical mechanics? From my understanding, heat capacity is an extensible property so any change in the system would result...
2. ### I Derivation of ideal gas heat capacity relationship

The text derives C_p-C_v=nR for ideal gasses. They start with $$H = U + PV = U + nRT$$ for ideal gas. Since U is only a function of temperature for an ideal gas, the right-hand side is only a function of temperature so $$\frac{dH}{dT} = \frac{dU}{dT} + nR$$. Now the text does something I...
3. ### Deriving general specific heat capacity formula

For this, Dose anybody please know of a better way to derive the formula without having ##c = \frac{\Delta Q}{m \Delta T}## then taking the limit of both sides at ##\Delta T## approaches zero? I thought ##\Delta Q## like ##\Delta W## was not physically meaningful since by definition ##Q## is...
4. ### Specific Heat Capacity of a metal bar placed into water

Previously solved thermal energy gained by water as Eth= 0.15(4180)(17.6) = 11035.2 J Not sure if its relevant
5. ### B Opening this jar is made easier by cooling or heating?

I've found this question online and don't agree with the explanation given. Explanation I disagree. If you heat the jar, the diameter of the top opening increases more than the diameter of the wooden lid, making it looser. The opposite happen if you cool the jar and the lid. Can you please...
6. ### I Understanding Heat Capacity and Work: Clarifying Misconceptions

In defining the heat capacity of a subatance as the constant relating change in temperature to change in heat, is it assumed that the system does no work? Does it really say (heat capacity is the constant relating heat change to temperature change when the system does no work)?
7. ### I Calculating the specific heat capacity for the 2D Ising model

So I'm looking at the book "Equilibrium Statistical physics" by Plischke and Bergersen. I'm doing the calculation of the specific heat of the 2D Ising model. I can't seen to quite get out the same expression as in the book - there are a coupe of minus signs that are different. I don't know if I...
8. ### A Molar heat capacity of CO2 is too high. Why?

At very high temperatures CO2 should have Cp = 15/2 R, since there are 3 translational, 2 rotational and 4 vibrational degrees of freedom. Experimental values are a bit higher than that, at least according to a figure I found on the internet. Is that correct? And what is the explanation? A...
9. ### Help understanding "Heat capacity"

Homework Statement:: First of, this is not a "homework" per say, since this is not in my curriculum. If you still want to help, see the description :) Relevant Equations:: C = Q/(delta T), where delta T is the raise in temperature in Kelvin and Q is the added heat energy I want to learn about...
10. ### Thermal physics question: Specific heat capacity

At first, I tried to calculate the heat energy required by doing this: I realized I should calculate heat energy separately instead of grouping glass and water together so I did this: But the answer is supposed to be 6.29 x 10^4. I don't know how to solve this. Can anyone help please? Thank you
11. ### Vaporization Heat and the Heat Capacity of H20 comparison

According to the Vaporization Heat table, the heat needed for 1 mol of H2O to evaporate at 100°C is 40.7KJ and 44.0KJ/mol is needed to evaporate H2O at 25°C. Thus 44.0-40.7=3.7KJ is the energy needed to heat H2O to 100°C from 25°C. However, according to the heat capacity of H2O, 3.7KJ will only...
12. ### I Heat capacity for a real gas using the ideal gas (zero pressure) equation

Summary:: Heat capacity for real gas with ideal gas (zero pressure) equation I'm looking at this problem and I'm stuck. I usually question everything but this problem is confusing me. I don't know how they've made the jump from reduced properties (from generalized Cp charts(?)) to...
13. ### I Entropy and Heat Capacity Relation

I have a simple question sort of about exact differentials and deciding which variables matter and when. I know we can write entropy ##S## as ##S(P,T)## and ##S(V,T)## to derive different relations between heat capacities ##C_V## and ##C_P##. I was wondering if it is technically correct to...
14. ### A query about heat capacity and specific heat capacity

Homework Statement:: why does heat capacity depend on the mass/size of the object when it's units is J/K , and why is specific heat capacity dependent on the material/substance when it's unit is J/kgK? Relevant Equations:: Q=Cθ Q=mcθ -
15. ### Specific heat capacity & heat capacity

the answer is 1/2 , but when I did the working out, I got 2/1.. so I'm quite confused
16. ### Calculating specific heat capacity from entropy

Hey guys! I'm currently struggling with a specific thermodynamics problem. I'm given the entropy of a system (where ##A## is a constant with fitting physical units): $$S(U,V,N)=A(UVN)^{1/3}$$I'm asked to calculate the specific heat capacity at constant pressure ##C_p## and at constant volume...
17. ### Find rate of temperature change using heat capacity, density and area

So first I found rate of heat change using the above equation, with T=883K, e=1, SA= 6*l^2=21.66 Now dQ/dt=746593.71 W Now I am not sure entirely what to do next. They give density so I likely have to get the mass from that, M=pV,=1.9^3*4037=27689.783 kg. My issue is that I don't know how to...

thanks!
19. ### Debye Approximation of Heat Capacity in 1D

So really i am just unsure how to answer the last part of the question. I am unsure how to apply the low and high temperature limits the way i have done it. Do i set upper/lower limits on the integral and solve? If so i am not sure what to put Here is what he book has for 3d
20. ### Heat Capacity of a Van Der Waals' gas in an Open system

In our class, we're using Wassermann's Thermal physics as textbook. I always try to solve all question which included in Text book. But sometime when I meet a problem that look like easy but actually hard, I'm so embarrassed. This problem do also. First, in the textbook grand potential for van...

32. ### Is Heat Capacity Derivable for Non-Ideal Liquid Mixtures?

Can I derive heat capacity of one phase mixture of three liquids as a sum of their mass shares multiplied by heat capacities of solitary components at given temperature? All components are miscible, of course ... thank you in advance

Not attempt
34. ### Molar specific heat capacity for constant volume.

Dear Experts, We compute Cv for gases using the idea of equipartition principle and degrees of freedom. In case of a diatomic molecule, there are minimum 3 degrees of freedom (at very low temperatures) and maximum 6 degrees of freedom one of them being vibrational (at high temperatures. Does it...
35. ### 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...
36. ### Heat Capacity energy exchange problem

Givens for water: m: 0.250kg of water TW : 95°C C=4180 Givens for mug: m=0.085kg TM : 19° c=107 Required: final temperature of water Analysis/Solution: Qreleased+Qabsorbed=0, q=mc▲t mw*cw*Tw + mp*cp*Tp = 0 (0.250)(4180) (T2-95) + (0.085)(107)(t2-19)=0 1045(t2-95) + 9.095(t2-19)=0...
37. ### Could you help me with this thermodynamics question?

So, I converted the V (milk) to m3 and found 1.8E-4 m3 and i already know the density so i found the mass of the milk in the bottle. Mmilk= 1.9E-7 kg Normally i would try to connect it with the formulas above but i don't know temperature. I am not sure how i can connect the dots. Can...

Attempt:
39. ### Finding heat capacity for liquids

liquid melting point (degrees C) boiling point (degrees C) water (H2O) 0 100 sodium (Na) 98 883 Sodium-potassium(NaK) -11 785 Lead(Pb) 327 1749 I'm prettttty sure by consulting the literature means by using the above table… but if that's the case then how in the world do you find Cv...
40. ### Capture and re-use the heat generated from Air Compression

I am trying to fill pipes with a volume of 556 cuft to 15,000 psi. I want to capture and re-use the heat generated from the compression process and re-use it. Is this amount of compression and heat exchanging possible with current technology
41. ### I Solution of the 1D heat equation

$$\frac{\partial T}{\partial t}=\alpha\frac{\partial^2 T}{\partial^2 t}$$ with an initial condition and boundary conditions $$T(x,0)=T_0$$ $$T(L,t)=T_0$$ $$-k\left.\frac{\partial T}{\partial x}\right|_{x=0}=2A\cos^2\left(\frac{\omega t}{2}\right)=A(\cos\omega t+1)$$ where $A=V_0^2/(8RhL)$...
42. ### How Does Newton's Law of Cooling Affect Heat Loss Calculations?

Homework Statement A metal ball of mass 1kg is heated by means of a 20W heater in a room at 20°C. The temperature of the ball becomes steady at 50°C. (a) Find the rate of loss of heat to the surrounding when the ball is at 50°C. fa) Assuming Newton's law of cooling, calculate the rate of loss...
43. ### Calculating Heat Capacity in a Bomb Calorimeter using Combustion of Toluene

Homework Statement The combustion of toluene has a ΔErxn of −3.91 × 103kJ/mol. When 1.70 g of toluene (C7H8) undergoes combustion in a bomb calorimeter, the temperature rises from 23.36 ∘C to 36.67 ∘C. Find the heat capacity of the bomb calorimeter to three sig-figs. Homework Equations q =...
44. ### Thermodynamics problem: Heat capacity of a Gas

Homework Statement In a certain process, a gas absorbs Q amount of heat and performs kQ amount of work, the molar heat capacity of the gas in terms of R, k and γ(Cp/Cv) is? Homework Equations U=Q+W U=nCvdT Q=CdT The Attempt at a Solution replacing U and Q with the above formulas and W from...
45. ### Heat capacity and temperature problem

Homework Statement A piece of metal is heated by supplying a constant power P. The temperature of the metal starts varying as T=kt. The heat capacity of the metal as a function of temperature is? Homework Equations Q=CdT The Attempt at a Solution From Q=CdT, dT is k, since P is Q/t, I plugged...
46. ### Heat Capacity relations for 1st order phase transition

Homework Statement Prove the following relation for which clausius equation holds : Cs=Cp-αV(ΔH/ΔV) Where Cs=∂q/∂T at constant S and is the heat capacity in the coexistence line of 2 phases Homework Equations dq=dU+dW dP/dT=ΔH/(ΔV*T) The Attempt at a Solution I do not fully understand why q...
47. ### Specific heat capacity of a solid material

Homework Statement A 4.80 kg piece of solid material is heated from 16.4C to 219C (3 s.f.) using 787 kJ of energy (3 s.f.). Assuming an efficiency of 0.383 for the heating process, and that the material does not melt, calculate the specific heat capacity of the material. Homework Equations...
48. ### Calculating Specific Heat Capacity

Homework Statement A 4.96 kg piece of solid material is heated from 16.7oC to 234oC (3 s.f.) using 725 kJ of energy (3 s.f.). Assuming an efficiency of 0.342 for the heating process, and that the material does not melt, calculate the specific heat capacity of the material. m = 4.96 kg change...
49. ### Understanding the Molar Heat Capacity of an Ideal Gas

We know that for an ideal gas the differential of the internal energy function is: dU = n Cv dT But is Cv the molar heat capacity or not?
50. ### (Specific) Heat capacity of brass at milliKelvin temperatures

Hi all, I do an calorimeter experiment at temperatures around 40 mK. To get more grip on the time constants that are associated with the heat flows, I calculate the thermal resistance as well as the heat capitance of the materials in the set-up. We assume that Newton's law of cooling is the...