A perfect gas undergoes the following three separate and distinct processes to execute a cycle (i) constant volume process during which 80 kJ of heat is supplied to the gas, (ii) constant pressure process during which 85 kJ of heat is lost to the surroundings and 20 kJ of work is done on it. (iii) adiabatic process which restores the gas back to its initial stage. Evaluate the work done during adiabatic process and the value of internal energy at all the state points if initially its value is 95 kJ.

A perfect gas undergoes the following three separate and distinct proc

1.	A perfect gas undergoes the following three separate and distinct processes to execute a cycle (i) constant volume process during which 80 kJ of heat is supplied to the gas, (ii) constant pressure process during which 85 kJ of heat is lost to the surroundings and 20 kJ of work is done on it. (iii) adiabatic process which restores the gas back to its initial stage. Evaluate the work done during adiabatic process and the value of internal energy at all the state points if initially its value is 95 kJ.
Answer» SOLUTION :This example illustrates the application of nonflow ENERGY equation and the 1st law applied to a cyclic process. Process 1 -2 : `Q_(1-2) = 80KJ, W_(1-2)=0` `U_(2)-U_(1)=Q_(1-2) -W_(1-2) ` `=80-0=80kJ` `U_(2)=80+95=175kJ` Process 2-3: `Q_(2-3)=-85kJ, W_(2-3)=-20kJ` `U_(3)-U_(2)=Q_(2-3)-W_(2-3)= -85-(-20)=-65kJ` `U_(3) = -65 +175 =110kJ` For the complete cycle : `oint delta Q = oint deltaW`. That is `Q_(1-2)+Q_(2-3) +Q_(3-1) =W_(1-2) +W_(2-3) +W_(3-1)` `80-85 +0=0 +(-20) +W_(3-1)` `:.` Work done during ADIABATIC process, `W_(3-1)=15kJ`