Work Done in Thermodynamic Process – Rankers Physics
Topic: Thermal Physics
Subtopic: Kinetic Theory of Gases

Work Done in Thermodynamic Process

In a thermodynamic process, pressure (in Pa) varies as, \(P = a + bV\) [where \(V\) represents volume in \(\text{m}^3\), \(a\) and \(b\) are constants]. The work done by gas during expansion from \(2 \text{m}^3\) to \(3 \text{m}^3\) will be
\(\left(\frac{3a}{2} + b \right) \text{J}\)
\(\left(a + \frac{5b}{2}\right) \text{J}\)
\(\left(b + \frac{5a}{2}\right) \text{J}\)
Zero

Solution:

Work done \(W = \int_{V_1}^{V_2} P dV = \int_2^3 (a+bV) dV = \left[aV + \frac{bV^2}{2}\right]_2^3 = a(3-2) + \frac{b}{2}(9-4) = a + \frac{5b}{2}\).

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