CALC Two moles of an ideal gas are compressed in a cylinder at a constant temperature of 65.0o C until the original pressure has tripled. (a) Sketch a pV-diagram for this process. (b) Calculate the amount of work done.
Solution 3E The ideal gas is compressed here and its pressure has tripled. It means that a work is done on the system. (a) The pV diagram can be drawn as shown below. Original pressure of the gas has tripled. This means the volume of the gas will become one third of the initial value. Let. initial pressure P = P 1 Initial volume V = V 1 Final pressure P 2 = 3P P V Final volume V 2= P 1 2 V = PV 2 3P V 2= V /3 (b) The compression of the gas happens at constant temperature. So, this is an isothermal process. V 2 Now, work done in an isothermal process is given by W = nRT dV …..(1), where n is V V 1 the number of moles of the gas, R is the gas constant and T is the absolute temperature. Given that, n = 2 T = 65 C = 273 + 65 K = 338 K Therefore, from equation (1), work done is V 2 W = 2 × 8.314 J/mol.K × 338 K × dV V V 1 V /3 dV W = 2 × 8.314 J/mol.K × 338 K × V V V /3 W = 5620 J × ln V W = 5620 J × ln 3 W = 5620 J × ( 1.1) W = 6182 J Therefore, the amount of work done is 6182 J. The negative sign indicates that work is done on the gas as it is compressed.