$A$ gas is compressed from a volume of $2 \,m^3$ to a volume of $1 \,m^3$ at a constant pressure of $100 \,N m^{-2}$. Then it is heated at constant volume by supplying $150 \,J$ of energy. As a result,the internal energy of the gas

The internal energy of the air in a room of volume $V$ at temperature $T$,with outside pressure $P$ increasing linearly with time,varies as

$A$ gas of mass '$m$' and molecular weight '$M$' is flowing in an insulated tube with a velocity '$2V$'. If the flow of the gas is suddenly stopped and all the kinetic energy is utilized to compress the gas,the increase in the temperature of the gas is ($\gamma$ is the ratio of specific heats,$R$ is the universal gas constant).

$A$ cyclic process $ABCA$ is shown in the $PT$ diagram. When presented on a $PV$ diagram,it would be:

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ With the increase in the pressure of an ideal gas,the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
Reason $(R) :$ In isothermal process,$PV =$ constant,while in adiabatic process $PV^\gamma =$ constant. Here $\gamma$ is the ratio of specific heats,$P$ is the pressure and $V$ is the volume of the ideal gas. In the light of the above statements,choose the correct answer from the options given below $:$

An ideal gas,initially in state $(P_{12}, V_1, T_1)$ is expanded isobarically to $(P_{12}, V_2, T_2)$,then adiabatically to $(P_{34}, V_3, T_3)$. It is then contracted isobarically to $(P_{34}, V_4, T_4)$ and finally adiabatically back to the initial state. The efficiency of this cycle is