In an ideal gas at temperature $T$, the average force that a molecule applies on the walls of a closed container depends on $T$ as $\mathrm{T}^{\mathrm{x}}$. The value of $x$ is

Heat engine operating between temperature $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by 62 K , its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ respectively are

The absolute temperature of a gas is determined by

When a system is taken from state ' $a$ ' to state ' $c$ ' along a path abc, it is found that $\mathrm{Q}=80 \mathrm{cal}$ and $\mathrm{W}=35 \mathrm{cal}$. Along path adc $\mathrm{Q}=65 \mathrm{cal}$ the work done W along path adc is