$A$ heat engine is involved with an exchange of heat of $1915\, J,$ $-40\, J,$ $+125\, J,$ and $-Q\, J$ during one cycle,achieving an efficiency of $50.0 \%$. The value of $Q$ is ....... $J$.

Answer the following questions based on the $P-T$ phase diagram of $CO_{2}$:
$(a)$ $CO_{2}$ at $1 \; atm$ pressure and temperature $-60^{\circ} C$ is compressed isothermally. Does it go through a liquid phase?
$(b)$ What happens when $CO_{2}$ at $4 \; atm$ pressure is cooled from room temperature at constant pressure?
$(c)$ Describe qualitatively the changes in a given mass of solid $CO_{2}$ at $10 \; atm$ pressure and temperature $-65^{\circ} C$ as it is heated up to room temperature at constant pressure.
$(d)$ $CO_{2}$ is heated to a temperature $70^{\circ} C$ and compressed isothermally. What changes in its properties do you expect to observe?

$A$ cyclic process is shown in the $p-v$ diagram. Which of the following statement$(s)$ is/are true?

$10,000$ small balls,each of mass $1 \, g$,strike a surface of area $1 \, cm^2$ per second with a velocity of $100 \, m/s$ perpendicular to the surface. They rebound with the same velocity. What is the pressure exerted on the surface?

An ideal gas with pressure $P$,volume $V$ and temperature $T$ is expanded isothermally to a volume $2V$ and a final pressure $P_i$. The same gas is expanded adiabatically to a volume $2V$,the final pressure is $P_a$. In terms of the ratio of the two specific heats for the gas $\gamma$,the ratio $\frac{P_i}{P_a}$ is

In Column-$I$ processes and in Column-$II$ the first law of thermodynamics are given. Match them appropriately:

Column-$I$	Column-$II$
$(a)$ Adiabatic	$(i)$ $\Delta Q = \Delta U$
$(b)$ Isothermal	$(ii)$ $\Delta Q = \Delta W$
	$(iii)$ $\Delta U = -\Delta W$