What is molar heat capacity: Definition and 15 Discussions

The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. Alternatively, it is the heat capacity of a sample of the substance divided by the amount of substance of the sample; or also the specific heat capacity of the substance times its molar mass. The SI unit of molar heat capacity is joule per kelvin per mole, J⋅K−1⋅mol−1.
Like the specific heat, the measured molar heat capacity of a substance, especially a gas, may be significantly higher when the sample is allowed to expand as it is heated (at constant pressure, or isobaric) than when it is heated in a closed vessel that prevents expansion (at constant volume, or isochoric). The ratio between the two, however, is the same heat capacity ratio obtained from the corresponding specific heat capacities.
This property is most relevant in chemistry, when amounts of substances are often specified in moles rather than by mass or volume. The molar heat capacity generally increases with the molar mass, often varies with temperature and pressure, and is different for each state of matter. For example, at atmospheric pressure, the (isobaric) molar heat capacity of water just above the melting point is about 76 J⋅K−1⋅mol−1, but that of ice just below that point is about 37.84 J⋅K−1⋅mol−1. While the substance is undergoing a phase transition, such as melting or boiling, its molar heat capacity is technically infinite, because the heat goes into changing its state rather than raising its temperature. The concept is not appropriate for substances whose precise composition is not known, or whose molar mass is not well defined, such as polymers and oligomers of indeterminate molecular size.
A closely related property of a substance is the heat capacity per mole of atoms, or atom-molar heat capacity, in which the heat capacity of the sample is divided by the number of moles of atoms instead of moles of molecules. So, for example, the atom-molar heat capacity of water is 1/3 of its molar heat capacity, namely 25.3 J⋅K−1⋅mol−1.
In informal chemistry contexts, the molar heat capacity may be called just "heat capacity" or "specific heat". However, international standards now recommend that "specific heat capacity" always refer to capacity per unit of mass, to avoid possible confusion. Therefore, the word "molar", not "specific", should always be used for this quantity.

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  1. V

    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. Philip Koeck

    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...
  3. House

    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?
  4. N

    Molar heat capacity at constant pressure/volume

    Morning I am being stupid but cannot work out these problems: 1. Energy supplied to 2.0 moles of an ideal gas is 117J and it changes the temperature by 2.0K (at constant pressure).2. Calculate both molar heat capacities at constant P and V.3. Firstly, I divided 117J by 4 to get the energy...
  5. K

    Calculating molar heat capacity from electron contribution

    Homework Statement Silver has a Fermi energy of 5.48 eV. Calculate the electron contribution to the molar heat capacity at constant volume, Cv, of Silver at 300 K. Express your result as a multiple of R. Is the value of Cv due principally to the electrons? If not, to what is it due? ans...
  6. shrutiphysics

    Molar Heat Capacity: Find Value of k

    Homework Statement A diatomic ideal gas is heated at constant volume until its pressure is doubled. It is again heated at constant pressure until its volume is doubled. The molar heat capacity for the whole process is kR. Find the value of k. Homework Equations ans is k=19/6. p/t=constant...
  7. L

    Molar heat capacity at constant volume

    Hi everyone, If you know the temperature rise of 2 moles of an ideal gas when a known amount of energy is transferred to it as heat, (hence are able to calculate cv by dU/dT); is the molar heat capacity simply half this value as it is half the number of moles?
  8. E

    Molar heat capacity and Degrees of freedom

    Homework Statement The diagram shows the molar heat capacity of an ideal diatomic gas and the number of degrees of freedom at different temperatures. Explain why there are 3 discrete plateaus and why the curve is smooth and leaning between them. Homework Equations - The Attempt at a Solution...
  9. Saitama

    Thermodynamics: Finding the molar heat capacity

    Homework Statement An ideal gas has a molar heat capacity ##C_V## at constant volume. Find the molar heat capacity of this gas as a function of its volume ##V##, if the gas undergoes the following process: ##T=T_0e^{\alpha V}## here ##T_0## and ##\alpha## are constants.Homework Equations The...
  10. I

    Molar heat capacity in metals and ionic solids

    I am doing my revision and noticed that metals all have a molar heat capacity ~25 J/mol/K = 3R. Ionic solids such as NaCl and CaF2 however have different molar heat capacities. (~51 and 72 respectively) Why is this? there is no explination that my lecturer gave and I can't find it online but...
  11. I

    Heat integral and molar heat capacity?

    dQ = nCvdT if volume is constant. However, n = pV/RT. What I don't understand is, why are we thinking n as constant when doing the integral? I had two problems that involved this on a test I had today. At first I kept it constant and then changed n. But then I thought, wait... isn't there a T...
  12. Telemachus

    Molar heat capacity (Thermodynamics)

    Homework Statement Hi there. I'm having some trouble on solving this exercise, which you can find on Callen 2nd edition. A simple fundamental equation that exhibits some of the qualitative properties of typical crystaline solids is: u=Ae^{b(v-v_0)^2}s^{4/3}e^{s/3R} Where A,b, and v0 are...
  13. M

    Formulas for Molar Heat Capacity at Constant Pressure/Volume

    Homework Statement Just wanted to find some clarity regarding this subject. In my textbook, it states that Q = nCvdT for constant volume and Q = nCpdT for constant pressure. However, one of the TA's in my classes were telling us how dU = nCpdT for constant pressure and dU = nCvdT for...
  14. S

    Molar heat capacity for an ideal monoatomic gas

    A monatomic ideal gas undergoes a process in which the ratio of P to V at any instant is constant and equals to 1. What is the molar heat capacity of the gas? (A) 4R/2 (B) 3R/2 (C) 5R/2 (D) 0
  15. G

    Molar Heat Capacity at Constant Pressure Understanding

    If I apply 200 J of energy as heat to 4 moles of an ideal gas at constant pressure and the temperature rises by 4 K, then the molar heat capacity at constant pressure will be Cp = Q / (n * deltaT) = 200 / (4 x 4) = 12.5 J K mol Am I on the right lines here?