Molar heat capacity at constant volume

[LivvyS]

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 c_v by dU/dT); is the molar heat capacity simply half this value as it is half the number of moles?

 

[Bystander]

If the process takes place at constant volume, yes.

 

[LivvyS]

Thanks for the quick reply!
Is the same true of heat capacity at constant pressure?

 

[Chestermiller]

Thanks for the quick reply!
Is the same true of heat capacity at constant pressure?

Yes.

 

[sardar]

Hello,

That is correct. The molar heat capacity at constant volume, denoted as Cv, is defined as the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius at constant volume. In the case of an ideal gas, the internal energy (U) is directly proportional to the temperature (T), so the slope of the U-T graph is equal to Cv. Since you are considering 2 moles of the gas, the molar heat capacity would indeed be half of the value calculated for one mole. This is because the internal energy and temperature of the gas are directly related to the number of moles, so doubling the number of moles would result in double the internal energy and temperature change. I hope this helps clarify your understanding of molar heat capacity at constant volume. Let me know if you have any further questions.