An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency is doubled. The temperature of the source is $.........^{\circ}C$.

Lithium metal crystallises in a body-centred cubic $(BCC)$ crystal. If the length of the side of the unit cell of lithium is $351 \ pm$,the atomic radius of the lithium will be ............. $pm$.

In the visible region,the dispersive powers and the mean angular deviations for crown and flint glass prisms are $\omega, \omega'$ and $d, d'$ respectively. The condition for getting deviation without dispersion when the two prisms are combined is

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$ and the equation having roots $\frac{1-\alpha}{\alpha}$ and $\frac{1-\beta}{\beta}$ is $px^2+qx+r=0$,then $r=$

$A$ cylindrical metallic rod,in thermal contact with two heat reservoirs at its two ends,conducts an amount of heat $Q$ in time $t$. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. The amount of heat conducted by the new rod,when placed in thermal contact with the same two reservoirs in time $t$,is:

Pure hydrogen sulphide is stored in a tank of $100 \ L$ capacity at $20 \ ^oC$ and $2 \ atm$ pressure. The mass of the gas will be ................. $g$.