Question

Temperature and volume curves are drawn for two thermodynamic processes. For the first process, it is a straight line and for the second, it is a rectangular hyperbola. The ratio of work done in the first process to the work done in the second process is

• A. 2:1
• B. 3:1
• C. 4:1
• D. 3:2

Answer 1

Answer: (A)

The first process is a constant pressure process, hence
w₁ = nR(2T₀ - T₀) = nRT₀

The equation for the second process is
$\text{T}=\frac{\text{c}}{\text{V}}$
Hence, $\text{P}=\frac{\text{nRT}}{\text{V}}=\frac{\text{nRc}}{{\text{V}}^2}$
$\therefore \text{w}={\int }_{{\text{V}}_0}^{2{\text{V}}_0}\text{PdV}=\frac{{\text{nRT}}_0}{2}$
$\therefore \frac{{\text{w}}_1}{{\text{w}}_2}=2\text{:}1$
∴ 2 : 1