Work done in adiabatic expansion of polyatomic gas – Rankers Physics

Thermodynamics: Practice Problem & Solution

The work done by 2 moles of polyatomic gas (\(\gamma = \frac{4}{3}\)) initially at room temperature to increase its volume eight times during adiabatic process will be (Take \(R = 2\text{ cal mol}^{-1}\text{ K}^{-1}\) and room temperature 27°C)
900 cal
600 cal
1800 cal
1200 cal

Solution Explained:

To solve this problem, we apply the core principles of Thermodynamics. Understanding the underlying formula is key to arriving at the correct answer below:

First, find final temperature: \(T_2 = T_1 \left(\frac{V_1}{V_2}\right)^{\gamma-1} = 300 \left(\frac{1}{8}\right)^{1/3} = 150\text{ K}\). Then work done \(W = \frac{nR(T_1 - T_2)}{\gamma-1} = \frac{2 \times 2 \times (300 - 150)}{1/3} = 1200\text{ cal}\).

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