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A Carnot engine cycle is shown in the Fig. (2). The cycle runs between temperatures \( T_{H}=\alpha T_{0} \) and \( \mathrm{T}_{\mathrm{L}}=\mathrm{T}_{0}(\alpha1) \). Minimum and maximum volume at state 1 and state 3 are \( \mathrm{V}_{0} \) and \( \mathrm{nV}_{0} \) respectively. The cycle uses one mole of an ideal gas with \( \mathrm{C}_{P} / C_{V}=\gamma \). Here \( C_{P} \) and \( C_{v} \) are the specific heats at constant
\( \mathrm{P} \) pressure and volume respectively. You must express all answers in terms of the given parameters \( \left\{\alpha, \mathrm{n}, \mathrm{T}_{0}, \mathrm{~V}_{0}, ?\right\} \) and universal gas constant \( \mathrm{R} \).
W
- Calculate the work done by the engine in each process: \( W_{12}, W_{23}, W_{34}, W_{41} \).
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