Question

In a thermodynamical process, $P = kV^3$. The work done when the temperature changes from 100°C to 300°C will be ________ nR.

Hint:

The general formula for work $W = \frac{P_1V_1 - P_2V_2}{n-1}$ is extremely useful for any process defined by $PV^n = \text{constant}$.

Answer 1

Correct Answer: 50

Step 1: Given $P = kV^3 \Rightarrow PV^{-3} = k$. This is a polytropic process $PV^n = C$ with $n = -3$.
Step 2: Work done in a polytropic process: $W = \frac{nR(T_1 - T_2)}{n - 1}$.
Step 3: $T_1 = 100 + 273 = 373$ K, $T_2 = 300 + 273 = 573$ K. $\Delta T = 200$ K.
Step 4: $W = \frac{nR(T_1 - T_2)}{-3 - 1} = \frac{nR(-200)}{-4} = 50 nR$.
Step 5: Value is 50.