From Figure 1.14 (a), let us assume that a heat engine receives heat QH from high temperature reservoir and converts it into work rejecting no heat to sink, thus violating Kelvin–Plank’s statement. Refrigerator receives heat QL from low temperature reservoir and supplies an amount (QH + QL) to high temperature reservoir when W = QH work is supplied to it. Thus, it operates to conform Clausius statement. But, from Figure 1.14 (b), it can be observed that heat QH follows a loop though HE and HP and perform no function. The equivalent system thus can be shown as figure. From Figure 1.14 (c), it is obvious the heat is being transferred from low temperature thermal energy reservoir to high temperature thermal energy reservoir, without any external work. It is therefore violation of Clausius statement. Thus, violation of Kelvin–Plank’s and we can say, the two statements are equivalent.
Figure 1.14 Violation of Clausius Statement by Violating Kelvin–Plank’s Statement
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