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) ?

One mole of a monoatomic ideal gas undergoes a quasistatic process, which is depicted by a straight line joining points $$({V_0},{T_0})$$ and $$({2V_0},{3T_0})$$ in a V-T diagram. What is the value of the heat capacity of the gas at the point $$({V_0},{T_0})$$?

For an ideal gas with initial pressure and volume p_i and V_i respectively, a reversible isothermal expansion happens, when its volume becomes V₀. Then, it is compressed to its original volume V_i by a reversible adiabatic process. If the final pressure is p_f, then which of the following statement(s) is/are true?

Temperature of an ideal gas, initially at 27$$^\circ$$C, is raised by 6$$^\circ$$C. The rms velocity of the gas molecules will