Question

Two moles of an ideal monoatomic gas is taken through a cycle ABCA as shown in the P-T diagram. During the process AB, pressure and temperature of the gas vary such that $PT=$ constant. If $T_1=300K$ calculate.
(a) work done on the gas in the process AB and
(b) the heat absorbed or released by the gas in each of the processes.
Give answers in terms of gas constant $R$

Answer 1

$Q=U+w$

$T=\frac{PV}{nR}$

$\Rightarrow \frac{P^{2}V}{nR}=x$

$\Rightarrow P{V}^{\frac{1}{2}}=\cos x$

$n=\frac{1}{2}$

$w=\frac{nR△T}{n-1}$

$=\frac{2RT}{-\frac{1}{2}}$

$=-4RT$.