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  4. 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 (V0 , T0) and (2 V0 , 2 T0) , 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 <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-fo84ew82ncpp.png />

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Q. 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 $\left(V_{0} , T_{0}\right)$ and $\left(2 V_{0} , 2 T_{0}\right)$ , 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



Question

NTA AbhyasNTA Abhyas 2020Thermodynamics

Solution:

Solution
Solution
The first process is the constant pressure process Hence, $w_{1}=nR\left(\right.2T_{0}-T_{0}\left.\right)=nRT_{0}$
Equation of the second process is $\text{T} = \frac{\text{c}}{\text{V}}$
Hence, $\text{P} = \frac{\text{nRT}}{\text{V}} = \frac{\text{nRc}}{\text{V}^{2}}$
$\therefore \text{w} = \displaystyle \int _{\text{V}_{0}}^{2 \text{V}_{0}} \text{PdV} = \frac{\text{nRT}_{0}}{2}$
$\therefore \frac{\text{w}_{1}}{\text{w}_{2}} = 2 \text{: } 1$