Question

An amount $Q$ of heat is added to a atomic ideal gas in a process in which the gas performs a work $\frac{2Q}{3}$on its surrounding. Find the molar heat capacity for the process.

Answer 1

Q = Amt of heat given

$\frac{q}{2}△q=w+△u$

$△u=q-\frac{q}{2}=\frac{q}{2}$

$v=n\frac{3}{2}RT=\frac{q}{2}=nT\times \frac{3}{2}R=3R\times nT$

Again Q = n CpdT Where C_P > Molar heat capacity at const. pressure.

3RnT = ndTC_P => C_P = 3R