# Work done under constant pressure

Work done under a constant pressure.

I know $$\Delta U = \Delta V \times \pi_T + C_V\Delta T$$

I thought I can give a try to find work done from above equation under constant pressure for an ideal gas.

$$q_p + w_p = C_V\Delta T$$ $$\implies C_p\Delta T + w_p = C_V \Delta T$$

$$\implies w_p = -\Delta T (C_p - C_V)$$ $$\implies w_p = - R\Delta T$$

Adiabatic work is $w_\mathrm{ad} = C_V \Delta T$

For a adiabatic work under constant pressure $w_\mathrm{ad} = w_{q} \implies C_V = -R \implies C_p = 2R$

Constant $C_p, C_V$ and negative $\gamma$ does not look correct to me.

• Which of my steps are incorrect ?

• So I should use Kirchoff's law to determine $q_p$ ? – A---B Feb 13 '17 at 11:03
• Ok I will try that out. Is my statement, $w_p = - R\Delta T$, correct for work done under constant pressure for an ideal gas ? – A---B Feb 13 '17 at 13:23