Six moles of an ideal gas perform a cycle shown in the figure. If the temperatures are $T_A = 600\, K,$ $T_B = 800\, K,$ $T_C = 2200\, K,$ and $T_D = 1200\, K,$ then the work done per cycle is approximately ...... $kJ$.

$A$ cylinder made of perfectly non-conducting material,closed at both ends,is divided into two equal parts by a heat-proof piston. Both parts of the cylinder contain the same mass of a gas at a temperature $t_0 = 27^{\circ}C$ and pressure $P_0 = 1 \text{ atm}$. If the gas in one of the parts is slowly heated to $t = 57^{\circ}C$ while the temperature of the first part is maintained at $t_0$,the distance moved by the piston from the middle of the cylinder will be $x \text{ cm}$. Find $x$ (total length of the cylinder $= 84 \text{ cm}$).

$10,000$ 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?

The relation between the efficiency $\eta$ of a heat engine and the coefficient of performance $\alpha$ of a refrigerator is:

Which of the following statements is correct regarding the $p-V$ graph?
$1$. The slope of the $p-V$ graph in an isothermal process is $-\frac{p}{V}$.
$2$. The slope of the $p-V$ graph in an adiabatic process is $-\frac{p}{V}$.
$3$. The slope of the $p-V$ graph in an isochoric process is $-\frac{\gamma p}{V}$.
$4$. The slope of the $p-V$ graph in an isobaric process is zero.

The ratio of the work done, change in internal energy, and heat absorbed when a diatomic gas expands at constant pressure is