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

Given below are two statements: One is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$.

Assertion A: Houses made of concrete roofs overlaid with foam keep the room hotter during summer.

Reason R: The layer of foam insulation prohibits heat transfer, as it contains air pockets.

In the light of the above statements, choose the correct answer from the options given below.

The equilibrium state of a thermodynamic system is described by

A. Pressure

B. Total heat

C. Temperature

D. Volume

E. Work done

Choose the most appropriate answer from the options given below.

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):