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  4. Temperature and volume curves are drawn for two thermodynamic processes. For the first process, it is a straight line and for the second, it is a rectangular hyperbola. The ratio of work done in the first process to the work done in the second process is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-mm9qo0mn3ms3.png />

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Q. Temperature and volume curves are drawn for two thermodynamic processes. For the first process, it is a straight line and for the second, it is a rectangular hyperbola. The ratio of work done in the first process to the work done in the second process is

Question

NTA AbhyasNTA Abhyas 2020Thermodynamics

Solution:

Solution
The first process is a constant pressure process, hence
w1 = nR(2T0 - T0) = nRT0
Solution
The equation for the second process is
$\text{T} = \frac{\text{c}}{\text{V}}$
Hence, $\text{P} = \frac{\text{nRT}}{\text{V}} = \frac{\text{nRc}}{\text{V}^{2}}$
$∴ \, \text{w} = \displaystyle \int _{\text{V}_{0}}^{2 \text{V}_{0}} \text{PdV} = \frac{\text{nRT}_{0}}{2}$
$∴ \, \, \, \frac{\text{w}_{1}}{\text{w}_{2}} = 2 \, \text{:} 1$
∴ 2 : 1