1. The ideal gas law is often written as: PV = RT where P, V and T are pressure,
ID: 1771107 • Letter: 1
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1. The ideal gas law is often written as: PV = RT where P, V and T are pressure, volume, and temperature of the gas, respectively. R is the ideal gas constant. The quantity S -cv In(PV) const is known as the entropy of the gas. Here, cv is the specific heat at constant volume and = (cv + R)/CV An engine is essentially a device to convert heat energy into mechanical work. (The heat energy may be generated by various means, of course, including by burning fuel.) In addition, engines must work in cycles that repeat. One of the most fundamental of these is known as the Carnot cycle. The Carnot cycle consists of two curves (C1 and C3 in Fig. 1) that are isothermal (V changes at constant T) and two curves (C2 and C4 in Fig. 1) that are isentropic (V changes at constant S). Let C C1U C2 U C3 U C4 be a contour on the PV-plane with negative orientation The total work W fc PdV is done by the engine when the state of the gas traverses the contour C. Use Greens theorem to convert this to an area integral, and by changing variables from P and V to T and S, show that the total work done in one Carnot cycle is W = R(Thigh-Tow) In T=Thigh T-T lowI C4 C3 Figure 1: Carnot cycleExplanation / Answer
Carnot cycle is an ideal 100% efficient engine. Read the text above for the understanding of each process.
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