[Physics] Formula for Work during Adiabatic process, should specific heat $c_p$ or $C_v$ be used

thermodynamicswork

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?

EDIT:

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.

OR

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

Best Answer

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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