A copper sphere cools from $$82^{\circ} \mathrm{C}$$ to $$50^{\circ} \mathrm{C}$$ in 10 minutes and to $$42^{\circ} \mathrm{C}$$ in the next $$10 \mathrm{~min}$$. Calculate the temperature of the surrounding?

Two gases occupy two containers $$A$$ and $$B$$. The gas in $$A$$ of volume $$0.20 \mathrm{~m}^3$$, exerts a pressure of $$1.40 \mathrm{~MPa}$$ and that in $$B$$, of volume $$0.30 \mathrm{~m}^3$$ exerts a pressure of $$0.7 \mathrm{~MPa}$$. The two containers and united by a tube of negligible volume and the gases are allowed to exchange. Then, if the temperature remains constants. the final pressure in the container will be (in MPa).

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