Suppose that 132 moles of a monatomic ideal gas is initially contained in a piston with...

3.8 Ratings (544 Votes)

Using ideal gas law;PV=nRT; P=nRT/V;Therefore P=406312.3253Pa;

energy transferred into the gas from the hot reservoir=nRT_H*ln(3.38/0.94)=1494430.595J;

energy transferred out of the gas into the cold reservoir=nRTc*ln(3.38/0.94)=488779.9316J;

Work done=Heat supplied-Heat rejected=1494430.595-488779.9316=1005650.663J;

Efficiency=work done/heat supplied = 1005650.663/1494430.595=67.29%;

Carnot efficiency = 1- Tc/T_H=1-(348/1064)=67.29%;

Q2;

Using PV=nRT;

T1=36.85K; T2=120.62K; T3=770.09K; T4=235.30K;

Using first law of Thermodynamics:Energy supplied(Q)=Change in internal Energy(U)+Work done by the system(W);

That is:Q=U+W;

U=nCv*(change in temperature);

W=P*(change in volume);

U1=584982.664J; W1=0; Q1=584982.664J;

U2=4535378.904J; W2=3024000J; Q2=7559378.904J;

U3=-3734545.53J; W3=0; Q3=-3734545.53J

U4=-1385816.04J W4=-924000J; Q4=-2309816.04J;

energy transferred into the gas from the hot reservoir=sum of +ve Q's=8144361.568J;

energy transferred out of the gas into the cold reservoir=sum of -ve Q's= 6044361.57J;

Work done = W1+W2+W3+W4=2100000J;

Efficiency = Work done/Energy supplied=2100000/8144361.568=25.78%

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