0.5 mole of an ideal gas at constant temperature $$27^{\circ} \mathrm{C}$$ kept inside a cylinder of length $$L$$ and cross-section $$A$$ closed by a massless piston. The cylinder is attached with a conducting rod of length L$$_1$$ cross-section area $$(1 / 9) \mathrm{m}^2$$ and thermal conductivity $$k_1$$ whose other end is maintained at $$0^{\circ} \mathrm{C}$$. If piston is moved such that rate of heat flow through the conduction rod is constant then velocity of piston when it is at height $$L / 2$$ from the bottom of cylinder is (neglect any kind of heat loss from system)

An electrically heated coil is immersed in a calorimeter containing $$360 \mathrm{~g}$$ of water at $$10^{\circ} \mathrm{C}$$. The coil consumes energy at the rate of $$90 \mathrm{~W}$$. The water equivalent of calorimeter and coil is $$40 \mathrm{~g}$$. The temperature of water after $$10 \mathrm{~min}$$ is

If 2 moles of an ideal monoatomic gas at temperature $$T_0$$ is mixed with 4 moles of another ideal monoatomic gas at temperature $$2 T_0$$, then the temperature of the mixture is

If the ratio of specific heat of a gas at constant pressure to that at constant volume is $$\gamma$$, the change in internal energy of the given mass of gas, when the volume changes from $$V$$ to $$2 V$$ at constant pressure $$p$$ is