# Thermodynamics : Joule Cycle

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A Joule cycle consists of two adiabats and two isobars: 1--> 2 and 3 ---> 4 are adiabatic compression and expansion respectively; 2 ---> 3 and 4 ---> 1 are constant pressure expansion and compression respectively. Treat the working medium as an ideal gas with constant gamma = Cp/Cv. Note that all temperatures T1,T2,T3 and T4 and the volumes V1,V2,V3 and V4 are different.

a) Draw a P-V diagram illustrating the Joule Cycle.

b) What is the heat absorbed Q during the process 2 ---> 3?

c) Calculate the work done of a Joule cycle.

d) Compute the efficiency of this cycle in terms of gamma and pressure ratio P1/P2, where P1 is the pressure at state 1 and P2 is the pressure at state 2.

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#### Solution Preview

Please refer to the attachment.

a) PV diagram is drawn above. During 1-2, the gas is compressed from volume V1 to V2 (V2 < V1) adiabatically (no heat enters or leaves the system) with corresponding increase of pressure from P1 to P2.

During 2-3, the gas expands from volume V2 to V3 (V3 > V2) at constant pressure P2.

During 3-4, the gas expands from volume V3 to V4 (V4 > V3) adiabatically (no heat enters or leaves the system) with corresponding decrease of pressure from P2 to P1.

b) Heat entering the system during 2-3 = Q1 = nCp(T3 - T2) where n = no. of moles of the gas, Cp = specific heat at constant pressure

Vf

c) Work done in general is given by : W = ∫PdV where Vi & Vf are the initial and final

Vi

volumes. In case of an adiabatic change PVγ = Constant (K) or P = K/Vγ. Hence, work ...

#### Solution Summary

The expert examines the thermodynamics of Joule Cycles. The work done is determined.