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.

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 $c=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ ).

A current carrying circular loop of radius 2 cm with unit normal $\hat{n}=\frac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\vec{B}=B_o(3 \hat{i}+2 \hat{k})$. If $B_o=4 \times 10^{-3} \mathrm{~T}$ and current $I=100 \sqrt{2} \mathrm{~A}$, the torque experienced by the loop is $\_\_\_\_$ Wb.A. ( $\pi=3.14$ )