First slide

Thermodynamic processes

Question

Find the work done by an ideal gas during a closed cycle 1 – 4 – 3 – 2 – 1 as shown if P₁ = 10⁵ Pa, P₀ = 3 $\times$ 10⁵ Pa, P₂ = 4 $\times$ 10⁵ Pa, V₂ – V₁ = 100 litre and segments 4 – 3 and 2 – 1 of the cycle are parallel to the V – axis.

Moderate

A

7500 J
B

8000 J
C

6000 J
D

None of these

Solution

Work done = Area 021 – Area 043
$\begin{array}{l} = \frac{1}{2} (V_{2} - V_{1}) (P_{0} - P_{0}) - \frac{1}{2} (V_{4} - V_{3}) (P_{2} - P_{0}) \\ = \frac{1}{2} (100 \times 10^{- 3}) (2 \times 10^{5}) - \frac{1}{2} [\frac{(P_{2} - P_{0})}{(P_{0} - P_{1})} (V_{2} - V_{1})] (P_{2} - P_{0}) \\ = 10^{4} - \frac{1}{2} [\frac{10^{5}}{2 \times 10^{5}} \times 100 \times 10^{- 3}] (10^{5}) J \\ = 10^{4} - 2500 = 7500 J \end{array}$

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