GOAL Use the adiabatic pressure vs. volume relation to find a change in pressure

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GOAL Use the adiabatic pressure vs. volume relation to find a change in pressure and the work done on a gas. PROBLEM A monatomic ideal gas at an initial pressure of 1.01 105 Pa expands adiabatically from an initial volume of 1.50 m3, doubling its volume. (a) Find the new pressure. (b) Sketch the PV diagram and estimate the work done on the gas. STRATEGY There isn't enough information to solve this problem with the ideal gas law. Instead, find the change in internal energy and use the given information to find the adiabatic index and the constant C for the process. For part (b), sketch the PV diagram and count boxes to estimate the area under the graph, which gives the work. SOLUTION (A) Find the new pressure. First, calculate the adiabatic index. ? = Cp = 5/2R = 5 Cv 3/2R 3 Find the constant C. C = P1V1? = (1.01 105 Pa)(1.50 m3)5/3 = 1.99 105 Pa

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