Question

Three moles of an ideal gas at $200$K and $2.0$ atm pressure undergo reversible adiabatic compression until the temperature becomes $250$K for the gas $C_v$ is $27.5J{K}^{-1}mo{l}^{-1}$ in this temperature range. Calculate q, w, $\delta U$, $\delta H$ and final V and final P.

Answer 1

$q=0$ (Adiabatic process)

$n=3$ $moles$

$\therefore △U=n{C}_V△T=2\times 27.5\times 50$

$\therefore △U=4125J$

Now, $△U=q+w$

$\therefore △U=w$

$\therefore w=4125J$

Now, $C_P-C_V=R$

$\therefore C_P=R+C_V=8.314+27.5=35.814Jmo{l}^{-1}{K}^{-1}$

$\therefore △H=n{C}_P△T=3\times 35.814\times 50=5372.1J$