Ten moles of an ideal monoatomic gas, initially in state at atmospheric pressure and temperature C, is enclosed in a metal cylinder of volume fitted with a frictionless piston. The gas is suddenly compressed to state with volume . Now, keeping the piston stationary, the cylinder is submerged in a water bath of temperature C until the gas reaches the temperature of the water bath, which is denoted as state . Finally, while still in the water bath, the piston is brought slowly to its initial position, which is denoted as state . If is universal gas constant, then the correct option(s) is/are: [Given: ]
- A
The schematic P-V diagram of the processes described above is:
- B
The change in internal energy in going from state to is .
- C
The net change in the internal energy in the whole process is .
- D
The pressure and temperature of the state are times the atmospheric pressure and K, respectively.
Process identification. is adiabatic compression, is isochoric cooling, is isothermal expansion. Option (A) matches.
State b temperature. For an adiabatic process with monoatomic gas, and const:
K.
State b pressure. const gives , not . Option (D) is incorrect.
Internal energy change . . Option (B) correct.
Net internal energy change. Since depends only on , and K (water bath at C K):
. Option (C) correct.
Correct options are (A), (B), (C).