Question

A Carnot cycle is conducted using an ideal diatomic gas. Initially, the gas is at temperature 25C., pressure of 100KPa and volume of 0.01m3. The system is then compressed isothermally to a volume 0.002m3. From that point, the gas undergoes an adiabatic compression ( with gamma= 1.4), until the volume further reduces to 0.001m3. After that, the system goes an isothermal expansion process to a point where the pressure of the system is 263.8KPa. Then the system continues the cycle with an adiabatic expansion.
a) What is the maximum pressure of gas in the cycle above ?
b) Calculate the maximum temperature in the above cycle.
c) Calculate the total work done in the cycle above
d) Calculate the total heat change in the cycle, then using the result from (c) calculate the efficiency of the cycle.

Answer 1

A) Using the Ideal gas equation.

P₁ V₁ = P₂ V_2.

100* 10_{​​​​​​}³ *0.01 =P₂*0.002

P₂ = 500*10³ pa.

B) Using the equation.

T₁ V₁^{- 1}= T₂ V₂^-1

25 *0.01^1.4-1 =T​2​_​​​​ *0.002^{1.4- 1}

^.   T₂ =125 C. (Ans)

C) Work done in isothermal compression is

W1 =Q1( heat) =nRT1 log(V2/V1) [ n=2, R =8.3]

W1=Q1 =-290.5J

W2 .=Q2 = n R (T1 -T2)/-1

W2 =Q2 =-4150 J

W3 =Q3 =nRT2 log (V3/V2)

W3 =Q3 =2* 8.3 *125 *-0.301

W3= Q3=- 624.5 J

W4 = Q4 =2R ( T2 -T1)/-1

W4 =Q4 =4150 J

D) Therefore total work done during the complete cycle is total heat produced

W= W1 +W2 +W3 +W4

= -290.5 -4150 -624.5 +4150

W= Q =747.5 J

Efficiency of the engine is. =1 -Q2/Q1=-13.28(Ans)