An ideal gas (Cp = 30J/mol K) passes through a gas turbine at a rate of 1.5 kmol

Question

An ideal gas (Cp = 30J/mol K) passes through a gas turbine at a rate of 1.5 kmol/s, where it is expanded adiabatically from 30.0 atm to 1.0 atm. The gas enters the turbine at 575K. What is the final temperature of the gas that leaves the turbine, and how much power does the turbine do?

An ideal gas (Cp 30J/mol K) passes through a gas turbine at a rate of 1.5 kmol/s, where it is expanded adiabatically from 30.0 atm to 1.0 atm. The gas enters the turbine at 575K. What is the final temperature of the gas that leaves the turbine, and how much power does the turbine do?

Explanation / Answer

Here first calculate gamma =Cp/Cv

We know Cp-Cv=R

Then Cv= 30-8.314=21.686

Gamma,g=30/21.686=1.383

We know for adiabatic ideal gas condition: T*P^((1-g)/g)= constant

(1-g)/g= -0.275

T1*P1^(-0.275)=T2*P2^(-0.275)

575*30^(-0.275)=T2*1^(-0.275)

T2 =225.66K

Work done =n*(R*T1-R*T2)/(g-1) = 1500*8.314*(575-225.66)/0.38 = 11464.786 kjoule

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