A piston cylinder system contained air is worked on carnot cycle to do some mechanical work initially,the system contains air at 1 bar,298k and0.01m^3. the system is first compressed until the volume is 0.002 m^3(isothermally). after that the system undergoes that the system undergoes an expansion process (isothermally) to a point where pressure in the system 5bar.at that point,the system is subjected to an isothermal expansion process until system reaches the initial state completing a cycle. calculate the net work done of the cycle and cycle efficiency
Answers
Explanation:
The net work done in a Carnot cycle is equal to the heat absorbed in the isothermal expansion process, minus the heat rejected in the isothermal compression process. The efficiency of a Carnot cycle is equal to the ratio of the net work done to the heat absorbed.
For an ideal gas, the work done during an isothermal process is given by the equation:
W = nRT ln(V2/V1)
Where n is the number of moles of gas, R is the gas constant, T is the absolute temperature, and V1 and V2 are the initial and final volumes.
Since the system is air at 1 bar and 298K, we can use the ideal gas law to find the number of moles of air in the cylinder:
PV = nRT
n = PV/RT
For V1 = 0.01 m^3 and P = 1 bar, we get:
n = 110^510^50.01/8.314298 = 0.851 moles
The work done during the isothermal compression is:
Wc = nRT ln(V2/V1) = 0.8518.314298*ln(0.002/0.01) = -44.98 J
The work done during the isothermal expansion is:
We = nRT ln(V2/V1) = 0.8518.314298*ln(0.01/0.002) = 89.97 J
The net work done in the cycle is:
Wnet = We - Wc = 89.97 - (-44.98) = 134.95 J
The efficiency of the Carnot cycle is given by:
η = Wnet / (Qh - Qc)
where Qh is the heat absorbed in the isothermal expansion process, and Qc is the heat rejected in the isothermal compression process.
Since the process is isothermal, Qh = Qc = nRT = 0.8518.314298 = 2265.9 J
Therefore, the efficiency of the Carnot cycle is:
η = Wnet / (Qh - Qc) = 134.95 / 2265.9 = 0.059 or 5.9%
So the cycle efficiency is around 5.9%