Consider the given diagram. An ideal gas is contained in a chamber (left) of volume V and is at an absolute temperature T. It is allowed to rush freely into the right chamber of volume V which is initially vacuum. The whole system is thermally isolated. What will be the final temperature of the equilibrium has been attained?

A horizontal fire hose with a nozzle of cross-sectional area $${5 \over {\sqrt {21} }} \times {10^{ - 3}}{m^2}$$ delivers a cubic metre of water in 10s. What will be the maximum possible increase in the temperature of water while it hits a rigid wall (neglecting the effect of gravity)?

Two identical blocks of ice move in opposite directions with equal speed and collide with each other. What will be the minimum speed required to make both the blocks melt completely, if the initial temperatures of the blocks were $$-$$8$$^\circ$$C each? (Specific heat of ice is 2100 Jkg^$$-$$1K^$$-$$1 and latent heat of fusion of ice is 3.36 $$ \times $$ 10⁵ Jkg^$$-$$1)

The water equivalent of a calorimeter is 10 g and it contains 50 g of water at 15$$^\circ$$C. Some amount of ice, initially at $$-$$ 10$$^\circ$$C is dropped in it and half of the ice melts till equilibrium is reached. What was the initial amount of ice that was dropped (when specific heat of ice = 0.5 cal gm^$$-$$1 $$^\circ$$C^$$-$$1, specific heat of water = 10 cal gm^$$-$$1 $$^\circ$$C^$$-$$1 and latent heat of melting of ice = 80 cal gm^$$-$$1) ?