One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is $4 \mathrm{~cm}^2$. The gas is heated slowly to raise the temperature by $1.2^{\circ} \mathrm{C}$ during which the piston moves by 25 mm . The amount of heat supplied to the gas is $\_\_\_\_$ J.

(Atmospheric pressure $=100 \mathrm{kPa}, R=8.3 \mathrm{~J} / \mathrm{mol} . \mathrm{K}$ ) (Neglect mass of the piston)

Initial pressure and volume of a monoatomic ideal gas are $P$ and $V$. The change in internal energy of this gas in adiabatic expansion to volume $V_{\text {final }}=27 \mathrm{~V}$ is $\_\_\_\_$ J.

The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If the length of the spring is cut to half, the same mass oscillates with frequency $v_2$. The value of $v_2 / v_1$ is $\_\_\_\_$ .

A monochromatic source of light operating at 15 kW emits $2.5 \times 10^{22}$ photons $/ \mathrm{s}$. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to $\_\_\_\_$。

(Take $h=6.6 \times 10^{-34} \mathrm{~J} . \mathrm{s}$ and $c=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ ).