For two thermodynamic process temperature and volume, diagrams are drawn. In the first process, it is a straight line having initial and final coordinates as V 0 , T 0 and 2 V 0 , 2 T 0 , whereas in s

Question

For two thermodynamic process temperature and volume, diagrams are drawn. In the first process, it is a straight line having initial and final coordinates as $(V_{0}, T_{0})$ and $(2 V_{0}, 2 T_{0})$ , whereas in second process it is a rectangular hyperbola having initial and final coordinates (V₀, T₀) and (2V₀, T₀/2). Then the ratio of work done in the two processes must be

TestHub · Accepted Answer

The first process is the constant pressure process Hence, $w_{1} = n R (2 T_{0} - T_{0}) = n R T_{0}$

Equation of the second process is $T = \frac{c}{V}$

Hence, $P = \frac{nRT}{V} = \frac{nRc}{V^{2}}$

$∴ w = \int_{V_{0}}^{2 V_{0}} PdV = \frac{{nRT}_{0}}{2}$

$∴ \frac{w_{1}}{w_{2}} = 2 : 1$

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