In calculating work during an adiabatic process I sometimes see two different equations being used. In one equation they use the specific heat $C_v$ and in another equation $c_p$ is used, why is that?

  1. $W = -C_v*(T_2 - T_1)$
  2. $w = -c_p*(T_e - T_i)$

When to use equation 1 and when to use equation 2?


I think if pressure is constant then to calculate the work $c_p$ should be used. In case the volume stays constant $C_v$ should be used.


When heat is leaving, $c_p$ should be used. When heat is entering $C_v$ should be used.

  • 1
    $\begingroup$ Welcome on Physics SE :) What have you thought about so far? What do you know about the difference between the two heat capacities? Please edit your question to reflect your own attempts at answering the question. $\endgroup$ – Sanya Oct 30 '16 at 14:14
  • $\begingroup$ Remember that in an adiabatic process $C_P/C_V=\gamma$. See here. $\endgroup$ – Charlie Oct 30 '16 at 14:25
  • $\begingroup$ Thank you both, I have edited my question. Hoping to get some clarification on when $c_p$ and when $C_V$ is used. $\endgroup$ – Ho Pam Oct 30 '16 at 14:50

Adiabatic process implies (from first law) that work done equals change in internal energy. If the system undergoing the process is an ideal gas, then change in internal energy is $C_v\Delta T$, irrespective of which process the system went through. This is so because internal energy of an ideal gas depends on temperature alone.

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