An ideal gas is made to undergo a cycle depicted by the $p-V$ diagram given below. The curved line from $A$ to $B$ is an adiabat. Then,

The slopes of isothermal and adiabatic curves are related as

$A$ gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $P_i = 10^5 \text{ Pa}$ and volume $V_i = 10^{-3} \text{ m}^3$ changes to a final state at $P_f = (1/32) \times 10^5 \text{ Pa}$ and $V_f = 8 \times 10^{-3} \text{ m}^3$ in an adiabatic quasi-static process, such that $P^3 V^5 = \text{constant}$. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at $P_i$, followed by an isochoric (isovolumetric) process at volume $V_f$. The amount of heat supplied to the system in the two-step process is approximately: (in $\text{ J}$)

Two containers $A$ and $B$ contain equal volumes of an identical gas at the same pressure and temperature. The gas in container $A$ is compressed to half its original volume isothermally,while the gas in container $B$ is compressed to half its original volume adiabatically. The ratio of the final pressure of gas in container $B$ to that of gas in container $A$ is

$10,000$ 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?

Heat is supplied to a diatomic gas at constant pressure. The ratio of $\Delta Q : \Delta U : \Delta W$ is