Question

A diatomic ideal gas undergoes a thermodynamic change according to the $P-V$ diagram showing figure. The total heat given to the gas is nearly in $N\times {10}^{-1}{P}_0{V}_0$ Find $N$ (use $\ell n2=0.7$ )

Answer 1

At A- $P_o{V}_o=R{T}_o$

From A to B-

At constant volume, pressure gets doubled.

And $P\propto T$

Hence, $T_B=2T_A=2T_o$

$Q_{AB}=\Delta U_{AB}+W_{AB}=C_v\Delta T+0$

$⟹Q_{AB}=\frac{5}{2}R(2T_o-T_o)=\frac{5}{2}{P}_o{V}_o=2.5P_o{V}_o$

From B to C-

$Q_{BC}=\Delta U+W_{BC}=0+R\left(2T_o\right)\ln \frac{2V_o}{V_o}=2R{T}_o\ln 2$

$=2\ln 2P_o{V}_o$

Hence , $Q=(2.5+2\ln 2)P_o{V}_o$

$⟹Q=3.9P_o{V}_o$