Question

In the following $P-V$ diagram two adiabatic cut two isothermals at temperature $T_1$ and $T_2$ (fig).
The value of $\frac{V_a}{V_d}$ will be

• A. $\frac{V_b}{V_c}$
• B. $\frac{V_c}{V_b}$
• C. $\frac{V_d}{V_a}$
• D. $V_b{V}_c$

Answer 1

The correct option is A $\frac{V_b}{V_c}$

$\text{Solution}:$

For adiabatic process

$T_1{V}_b^{\gamma -1}=constant$

For bc curve $T_1{V}_b^{\gamma -1}=T_2{V}_C^{\gamma -1}$ or $\frac{T_2}{T_1}={\frac{V_b}{V_c}}^{\gamma -1}$

For ad curve $T_1{V}_a^{\gamma -1}=T_2{V}_c^{\gamma -1}or\frac{T_2}{T_1}={\frac{V_a}{V_d}}^{\gamma -1}$

From equation (i) and (ii) ,

$\frac{V_b}{V_c}=\frac{V_a}{V_d}$

$\text{Hence A is the correct option}$