Question

An ideal gas is taken from the same initial pressure $P_1$ to the same final pressure $P_2$ by three different processes. If it is known that point $1$ corresponds to a reversible adiabatic and point $2$ corresponds to a single stage adiabatic then:

• A. Point $3$ may be a two stage adiabatic process
• B. The average $K.E.$ of the gas is maximum at point $1$
• C. Work done by surroundings in reaching points $1$ or $2$ will be positive
• D. The points $3$ and $4$ may lie along the process having $P{V}^2=$ constant

Answer 1

Answer: (C), (D)

The correct options are
C The points $3$ and $4$ may lie along the process having $P{V}^2=$ constant
D Work done by surroundings in reaching points $1$ or $2$ will be positive

During the adiabatic process, no heat enters or leaves the system. Hence during compression, the temperature will increase.

The work done in the reversible adiabatic process is given by the expression

$w_{rev}=\frac{nR}{\gamma -1}\times (T_2-T_1)$

Since, $T_2>T_1$ for the process in which the gas is taken from point 4 to point 1, the work done will be positive. In other words, work is done on the system.

Similarly, the work done will be positive when the system is taken from point 4 to point 2.

Hence option C is correct.

An ideal gas equation is $PV=nRT$. hence, $PV\times \frac{1}{T}=constant$

In the process when gas is taken from 4 to 3, as the volume decreases, the temperature increases.

Hence, it may be possible that $\frac{1}{T}\propto V$

Hence, it may be possible that $P{V}^2=constant$.

Thus, option D is correct.

Hence, the correct answers are option $\text{C}$ and $\text{D}$