Two rod of same area of cross-section have lengths $L$ and $2 L$ and coefficients of linear expansions $2 \alpha$ and $a$ respectively. If they are welded to form a composite rod of length $3 L$ then the coefficient of linear expansion of the composite rod is

For a given mass of a gas at constant temperature, the volume and the pressure are $V$ and $p$ respectively. Then the slope of the graph drawn between $\log _e V$ on $X$-axis and $\log _e p$ on $Y$-axis is

An ideal gas at $127^{\circ} \mathrm{C}$ is compressed suddenly to $8 / 27 \mathrm{}$of its initial volume. If $\gamma=5 / 3$ for an ideal gas, then rise in its temperature is

An insulating cylinder contains 4 moles of an ideal diatomic gas. When a heat $Q$ is supplied to it, 2 moles of the gas molecules dissociate. If the temperature of the gas remains constant, then the value of $Q$ is ( $R=$ universal gas constant)