a) A volume of compressed gas in a closed cylinder expands as a piston is withdrawn. The gas pressure is a function of the gas volume, P = P ( V ), and the force exerted by the gas on the piston is the product of the piston surface area and the gas pressure, f = R 2 P , where R is the cylinder radius. Show that the work done when the gas expands from volume V 1 to V 2 is W = R V 2 V x b) In a steam engine, the steam pressure P and volume V satisfy the relation PV 1 . 4 = k , where k is a positive constant. Note that when V increases, P decreases. Use part (a) to calculate the work done by the engine when the steam starts at pressure 1600 lb/in 2 and volume 100 in 3 and expands to volume 800 in 3 . Express the answer in ft-lb. V 1 P ( V ) dV . (hint: start from W = R b a f ( x ) dx , where x is the piston displacement as shown in the figure and f ( x

How do I set up question of the first part to derive the integral correctly?