Question

The P-T and V-T diagrams of an isochoric process of n moles of an ideal gas from pressure P${}_0$, volume V${}_0$ to pressure 4p${}_0$, indicating the pressures and temperatures of the gas in the initial and the final states will be

Answer 1

Using ideal gas equation at A: $P_o{V}_o=nR{T}_o$

$⟹$ $T_o=\frac{P_o{V}_o}{nR}$ ............(1)

The gas goes from initial state A to final state B via isochoric process i.e $V=V_o=constant$

$⟹$ $\frac{P_A}{T_A}=\frac{P_B}{T_B}$

OR $\frac{P_o}{T_o}=\frac{4P_o}{T_B}$ $⟹T_B=4T_o$

The V-T and P-T graphs are shown accordingly indicating the pressures and temperatures of the gas at A and B.