An ideal gas is heated from $27^{\circ} \mathrm{C}$ to $627^{\circ} \mathrm{C}$ at constant pressure. If initial volume of gas is $4 \mathrm{~m}^3$, then the final volume of the gas will be

Pressure of the gas remaining same, the temperature at which r. m. s. speed of the gas molecules is double its value at $27^{\circ} \mathrm{C}$ is

Rate of flow of heat through a cylindrical rod is $\mathrm{H}_1$. The temperature of the ends of the rod are ' $\mathrm{T}_1$ ' and ' $\mathrm{T}_2$ '. If all the dimensions of the rod become double and the temperature difference remains the same, the rate of flow of heat becomes ' $\mathrm{H}_2$ '. Then $\mathrm{H}_2=$

For which of the following combinations of working temperatures, the efficiency of Carnot's engine is maximum?