If two rods of length $$L$$ and $$2 L$$, having coefficients of linear expansion $$\alpha$$ and $$2 \alpha$$ respectively are connected end-to-end, then find the average coefficient of linear expansion of the composite rod.

A system is taken from state-A to state-B along two different paths. The heat absorbed and work done by the system along these two paths are Q$$_1$$, Q$$_2$$ and W$$_1$$, W$$_2$$ respectively, then

A gas ($$\gamma$$ = 1.5 ) is suddenly compressed to (1/4 )th its initial volume. Then, find the ratio of its final to initial pressure.

A cylinder has a piston at temperature of $$30 \Upsilon$$C. There is all round clearance of $$0.08 \mathrm{~mm}$$ between the piston and cylinder wall if internal diameter of the cylinder is $$15 \mathrm{~cm}$$. What is the temperature at which piston will fit into the cylinder exactly?

$$\left(\alpha_p=1.6 \times 10^{-5} / \Upsilon\mathrm{C} \text { and } \alpha_c=1.2 \times 10^{-5} / \Upsilon\mathrm{C}\right)$$