A piston-cylinder assembly has a constant cross sectional area of 0.05 m It cont

Question

A piston-cylinder assembly has a constant cross sectional area of 0.05 m It contains 1 mol of ideal gas. The initial pressure of the gas is 5 bar(abs). The initial temperature of the gas is 300 K. The constant-volume specific heat capacity of the ideal gas is 21 J/mol.K. The external pressure (with the unit of bar) is initially the same as the system pressure, and then changes according to 0.024942/V, where V (with the unit of m is the volume of the piston- cylinder assembly The final volume of the piston-cylinder assembly increases to 0.01 ms. The temperature of gas increases from 300K to 350 K during the expansion. (a) On a pressure-temperature diagram, clearly sketch out the initial and final state point of the system. Also sketch out the corresponding external pressure profile. Clearly show the initial and final values. (6 marks) (b) Calculate the heat input (in J) to the system. 6 marks) (c) on your pressure-temperature diagram in part (a), clearly sketch out the pathways by which you can calculate the enthalpy change (in J) of the ideal gas. Calculate the enthalpy change in J) of each of these pathways. 4 marks (d) For the pathways that you have sketched in part (c), calculate the entropy change of the ideal gas of each of those pathways. Hence, calculate the entropy change (in JK) of the ideal gas from the initial to the final state. (9 marks)

Explanation / Answer

a)    Initial state = 5 bar , 0.05 m3   , 300 K

     Final state =    3.5 bar , 0.06 m3   , 235.73 K

b) Heat input   = 1 * 8.314 * 300 * ln(0.06/0.05)

                         = 454.74 J

c)   enthalpy change =    454.74 - 5 * 21.21

                                  = 348.69 J

d) entropy change = H/T

                               =   348.69/300

                                = 1.1623 J/K

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