A container has two chambers of volumes V_1=2 litres and V_2=3 litres separated by a partition made of a thermal insulator. The chambers contains…

In an adiabatic process:

Two gases $A$ and $B$ are filled at the same pressure in separate cylinders with movable pistons of radius $r_A$ and $r_B$, respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas $A$ and $B$ are displaced by 16 cm and 9 cm , respectively. If the change in their internal energy is the same, then the ratio $\frac{r_A}{r_B}$ is equal to

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature $27^{\circ} \mathrm{C}$. The mass of the oxygen withdrawn from the cylinder is nearly equal to : [Given, $R=\frac{100}{12} \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$, and molecular mass of $O_2=32,1 \mathrm{~atm}$ pressure $\left.=1.01 \times 10^5 \mathrm{~N} / \mathrm{m}\right]$

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity $2 K$ while that in the middle has thermal conductivity $K$. The left end of the combination is maintained at temperature $3 T$ and the right end at $T$. The rods are thermally insulated from outside. In steady state, temperature at the left junction is $T_1$ and that at the right junction is $T_2$. The ratio $T_1 / T_2$ is 

According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant $\gamma=\frac{C_p}{C_v}$ is ( $C_P$ where $C_v$ are the specific heat capacities of the gas at constant pressure and constant volume, respectively):