# Example Problem with Complete Solution

7D-4 : ΔS and the T-S Diagram for Ideal Gas Processes 8 pts
 An ideal gas is contained in a piston-and-cylinder device in which the system moves from state 1 to state 2. a.) If T2 is greater than T1, show that the ΔS12 is greater if the process is isobaric than if it is isochoric. Sketch the isobaric and isochoric process paths on PV and TS diagrams. b.) Use your TS Diagram from part (a) to show that an isochoric path passing through a state has a greater slope than an isobaric path passing through the same state. c.) If P2 is greater than P1, show that the ratio of ΔS12 for an isothermal process to ΔS12 for an isochoric process is (1 - g).  Sketch the isothermal and isochoric proces paths on PV and TS diagrams. Read : Sketch the process in parts (a), (b) and (c) first to get a better understanding of the processes. For part (a) use equations relating entropy to Cp and CV. For part (b) recall that the slope on a TS Diagram is (dT/dS). For part (c) determine DS for each process and determine the ratio. Given: A closed system consisting of an ideal gas with constant specific heat ratio g. Find: Part (a) For the process where the T increases from T1 to T2: show that DS is greater if the change in state occurs at constant P than if it occurs at constant V. Sketch PV and TS Diagrams for the process. Part (b) Show on a TS Diagram that a line of constant specific volume passing through a state has a greater slope than a line of constant P. Part (c) For the process where the P increases from P1 to P2: show that the ratio of DS for an isothermal process to DS for a constant specific volume process is (1 - g).