Carnot Cycle Problem: An automobile engine works by burning gasoline in its cylinders

Chapter 11, Problem 9

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Carnot Cycle Problem: An automobile engine works by burning gasoline in its cylinders. Assume that a cylinder in a particular engine has diameter 2 in. (Figure 11-2i). When the spark plug fires, the pressure inside the cylinder is 1000 psi (pounds per square inch),and the volume is at its minimum, 1 in.3. As the piston goes out, the hot gases expandadiabatically (that is, without losing heat to thesurroundings). The pressure drops accordingto the equation p = k1V 1.4 Figure 11-2iwhere p is pressure, V is volume, and k1 is aproportionality constant. When the piston isfarthest out and the volume is 10 in.3, theexhaust valve opens and the pressure drops toatmospheric pressure 15 psi. As the pistoncomes back, the cool gases are compressedand the cycle is repeated. For compression, p = k2V 1.4, where k2 is a differentproportionality constant.a. Find the work done on the piston by theexpanding hot gas.b. Find the work done by the piston as itcompresses the cool gas.c. Find the net amount of work done. This isthe amount of work that is available formoving the car.d. How is Carnot pronounced? Who wasCarnot?