question 4 please. NOTE: it is (R/gamma) in the question I cut it off accidental

Question

question 4 please.

NOTE: it is (R/gamma) in the question I cut it off accidentally

The Otto cycle is a thermodynamic cycle that approximates a gasoline car engine. It consists of two isopycnal' legs ('isopycnal' means constant density, or 'isochoric' means constant volume), and two isentropic (constant molar entropy) legs. For the following, assume an ideal gas, with bar C_v constant. Comparing Delta bar S on the 2, 3 and 1, 4 legs, show that T_4/T_1 = T_3/T_2. Show that T/T_1 = [bar V_1/V]^gamma on 1, 2, and write the T(bar V) expression that holds on 3, 4. Show that the heat added to the system on 2, 3 is Delta bar Q_2, 3 = R/gamma (T_3 - T_2). Show that the work done to the system over the full cycle is Delta bar W = R/(T_4 - T_3 + T_2 - T_1).

Explanation / Answer

From PV diagram we can observe that, Process 2-3 and 1-4 are isochoric process(constant volume process) and from other diagram , the process 1-2 and 3-4 are constant entropy process and also adiabatic processs.

So, work done for 2-3 and 1-4 is zero (0) as it is constant volume

So, total work = work done during 1-2 and 3-4

W1-2 = (P2V2- P1V1 )/ Y

= R(T2-T1) /Y

Similarly,

W3-4 = (P4V4- P3V3 )/ Y

= R(T4 - T3) /Y

Total work done = R(T4 - T3) /Y + R(T2-T1) /Y

= R/Y ( (T4 - T3) + (T2-T1) )

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