A reversible heat engine carries `1 mol` of an ideal monatomic gas around the cycle `ABCA`, as shown in the diagram. The process `BC` is adiabatic. Call the processes `AB, BC` and `CA` as `1,2` and `3` and the heat `( DeltaQ)_(r)`, change in internal energy `(DeltaU)`, and work done `( DeltaW)_(r), r=1,2,3` respectively. The temperature at `A,B,C` are `T_(1)=300K,T_(2)=600K` and `T_(3)=455K`. Indicate the pressure and volume at `A,B` and` C` by `P_(r)` and `V_(r), r=1,2,3,` respectively. Assume that intially pressure `P_(1)=1.00atm.`
Which of the following represents the correct values for the quantities indicated ?

Options

A. `V_(1)=3 xx 10^(-3)Rm^(3), P_(2)=0.5 atm`
B. `V_(2)=3 xx 10^(-3)Rm^(3), P_(3)=1.0 atm`
C. `V_(3)=3 xx 10^(-3)Rm^(3), P_(2)=2.0 atm`
D. `V_(2)=3 xx 10^(-3)Rm^(3), P_(3)=2.0 atm`

Answer

B

Explanation

It is given that `P_(1)=1=1.013xx 10^(5)N//m^(20`
and `T_(1)=300K`
Hence
`V_(1)=(1xxRT)/(P_(1))=(Rxx300)/(1.013xx10^(5))m^(3)`
`=3 xx 10^(5)Rm^(3)`
Also
`P_(2)=(RT_(2))/(V_(2))=(RT_(2))/(V_(1))=((RT)/(V_(1)))xx(T_(2))/(T_(1))=2P_(1)=2 atm`
`V_(2)=V_(1)=3xx10^(-3)Rm^(3)`
`V_(3)!=3 xx 10^(-3)Rm^(3)`
Also `P_(3)=P_(1)=1 atm`