Show that P v k = constant and also the isentropic expansion exponent k reduces to the specific heat relation c p / c v for an ideal gas.

Question

Want to see the full answer?

Answer 1

Question

Chapter 12.6, Problem 88RP

To determine

Show that Pvk=constant and also the isentropic expansion exponent k reduces to the specific heat relation cp/cv for an ideal gas.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Two identical piston-cylinder devices are each filled with 1 kg air at T = 300 K and P = 2 bar. Next, one of the gases undergoes a reversible and isothermal expansion, and the other one expands isentropically. Both of the gases stop expanding when their final volumes reach twice of their initial volumes. [5] a) Sketch both of these processes on the same T-S plot. Indicate the direction of the expansion process on the plot. (No need to express the values for T and S on the plot) [5] b) Sketch both of these processes on the same P-V plot. Indicate the direction of the expansion process on the plot. (No need to express the values for P and V on the plot) [10] c) Calculate the heat transfer between the air and the surrounding for each process separately. show possible interpolations

One mole of an ideal gas, initially at 20 °C (293.15 K) and 1.50 bar, undergoes the following mechanically reversible changes. It is compressed isothermally to a point such that when it is heated at constant volume to 100 °C (373.15 K) its final pressure is 10 bar. Take Cp = (7/2)R and Cv = (5/2)R. Hints: Process 1 to 2: T1 = T2; Process 2 to 3: (P2/T2) = (P3/T3), thus (P2/T1) = (P3/T3) Use equations for isothermic and isochoric processes. Wtotal = W12 + W23 and Qtotal = Q12 + Q23. What is the amount of work involved in the process? What is the amount of heat transferred in the process?

One mole of an ideal gas, initially at 20 °C (293.15 K) and 1.50 bar, undergoes the following mechanically reversible changes. It is compressed isothermally to a point such that when it is heated at constant volume to 100 °C (373.15 K) its final pressure is 10 bar. Take Cp = (7/2)R and Cv = (5/2)R. Hints: Process 1 to 2: T1 = T2; Process 2 to 3: (P2/T2) = (P3/T3), thus (P2/T1) = (P3/T3) Use equations for isothermic and isochoric processes. Wtotal = W12 + W23 and Qtotal = Q12 + Q23. What is the change in internal energy? What is the change in enthalpy?