Rails of material of steel are laid with gaps to allow for thermal expansion. Each track is 10 m long, when laid at temperature $17^{\circ} \mathrm{C}$. The maximum temperature that can be reached is $45^{\circ} \mathrm{C}$. The gap to be kept between the two segments of railway track is

$$\left(\alpha_{\text {steel }}=1.3 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)$$

If the potential difference used to accelerate electrons is doubled. By what factor does the deBroglie wavelength $(\lambda)$ associated with the electrons change?

In an adiabatic process for an ideal gas, the relation between the universal gas constant ' $R$ ' and specific heat at constant volume ' $\mathrm{C}_{\mathrm{v}}$ ' is $R=0.4 C_v$. The pressure ' $P$ ' of the gas is proportional to the temperature ' $T$ ', of the gas as $T^k$. The value of constant ' K ' is

A p-n junction diode cannot be used