Question

One mole of a monoatomic ideal gas undergoes the process $A\to B$ in the given $P-V$ diagram. The specific heat for this process is

• A. $3R/2$
• B. $13R/6$
• C. $5R/2$
• D. $2R$

Answer 1

The correct option is B $13R/6$

$W=\underset{v_i}{\overset{v_f}{\int }}PdV$
Work done is area under $PV$ graph, ie area of trapezium,hence
$W=\frac{1}{2}(6P_0+3P_0)4V_0$
$W=18P_0{V}_0$
$\Delta U=\frac{P_f{V}_f-P_i{V}_i}{5/3-1}=\frac{30P_0{V}_0-3P_0{V}_0}{2/3}$
$=\frac{81P_0{V}_0}{2}$
$\Delta Q=W+\Delta U=\frac{117}{2}{P}_0{V}_0$
$nC(T_f-T_i)=\frac{117}{2}{P}_0{V}_0$
$C(\frac{6P_0\times 5V_0}{R}-\frac{3P_0{V}_0}{R})=\frac{117}{2}{P}_0{V}_0$
$C=\frac{\frac{117}{2}{P}_0{V}_0}{\frac{27P_0{V}_0}{R}}=\frac{13R}{6}$