Change of state: melting, boiling, latent heat: Practice Questions

A solid substance of mass \(m\) is heated continuously using a heater of constant power \(P\). The substance starts below its melting point and is monitored as it heats up and melts. The temperature of the solid increases by \(\Delta T\) over a time interval \(t_1\) until it reaches its melting point. It then takes a further time \(t_2\) for the entire substance to melt at constant temperature. Assume negligible heat loss to the surroundings.

If the specific heat capacity of the solid is \(c_s\) and the specific latent heat of fusion is \(l_f\), which of the following expressions correctly relates \(c_s\) to \(l_f\)?

A well-insulated calorimeter of negligible heat capacity contains \(0.30\text{ kg}\) of water at \(25^\circ\text{C}\). A block of ice of mass \(0.10\text{ kg}\) at \(-10^\circ\text{C}\) is added to the water. At the same time, a heater with a constant power of \(50\text{ W}\) is switched on to heat the mixture for \(8\text{ minutes}\).

Given:
Specific heat capacity of ice = \(2100\text{ J kg}^{-1}\ ^\circ\text{C}^{-1}\)
Specific heat capacity of water = \(4200\text{ J kg}^{-1}\ ^\circ\text{C}^{-1}\)
Specific latent heat of fusion of ice = \(3.34 \times 10^5\text{ J kg}^{-1}\)

What is the final temperature of the mixture at the end of the \(8\text{ minutes}\)?

A constant power heater is used to heat 1.0 kg of ice, initially at 0°C, in a container. The heater supplies heat at a constant rate P.

It takes 1000 s for the ice to completely melt into water at 0°C. During this melting phase, heat loss to the surroundings is considered negligible.

The water is then heated further for another 400 s. The temperature of the water rises from 0°C to 20.0°C. During this second heating phase, the container loses heat to the surroundings at a constant rate H.

Given: Specific latent heat of fusion of ice, \(L_f = 3.34 \times 10^5 \text{ J kg}^{-1}\). Specific heat capacity of water, \(c_w = 4200 \text{ J kg}^{-1} \text{ K}^{-1}\).

What is the constant rate of heat loss H from the container during the second heating phase?

A calorimeter of heat capacity \(120\text{ J K}^{-1}\) contains \(0.40\text{ kg}\) of water and \(0.15\text{ kg}\) of ice in thermal equilibrium at \(0^\circ\text{C}\). Dry steam at \(100^\circ\text{C}\) is passed into the mixture until the ice is completely melted and the final temperature of the system reaches \(30^\circ\text{C}\). What is the mass of steam that has condensed during this process?

Given: Specific heat capacity of water \(= 4200\text{ J kg}^{-1}\text{ K}^{-1}\), Specific latent heat of fusion of ice \(= 3.34 \times 10^5\text{ J kg}^{-1}\), Specific latent heat of vaporization of water \(= 2.26 \times 10^6\text{ J kg}^{-1}\).

A beaker of water is heated by a Bunsen burner until it boils at its boiling point of \( 100^\circ\text{C} \).

(a) State what happens to the temperature of the water as it continues to boil at a constant pressure.

(b) Compare the average kinetic energy of the water molecules in the liquid state and the steam state at this boiling point.

(c) Explain why the internal energy of the substance increases during boiling, in terms of the work done and molecular potential energy.

A student uses an immersion heater of power \(200\text{ W}\) to heat a mixture in a lagged calorimeter. The calorimeter initially contains \(0.4\text{ kg}\) of water at \(25^{\circ}\text{C}\). A block of ice of mass \(0.15\text{ kg}\) at \(-10^{\circ}\text{C}\) is added to the water, and the heater is switched on immediately.

Given:
Specific heat capacity of water \(c_w = 4200\text{ J kg}^{-1}\text{K}^{-1}\)
Specific heat capacity of ice \(c_i = 2100\text{ J kg}^{-1}\text{K}^{-1}\)
Specific latent heat of fusion of ice \(L_f = 3.34 \times 10^5\text{ J kg}^{-1}\)
Specific latent heat of vaporization of water \(L_v = 2.26 \times 10^6\text{ J kg}^{-1}\)

(a) Calculate the net energy provided by the heater to turn all the ice into water and bring the resulting mixture to a uniform temperature of \(0^{\circ}\text{C}\). (4 points)
(b) Determine the time taken for the system to reach the state described in part (a). (1 point)
(c) On a molecular level, explain why the specific latent heat of vaporization of water is significantly larger than its specific latent heat of fusion. (2 points)
(d) If the lagging of the calorimeter is removed and the room temperature is \(25^{\circ}\text{C}\), would the time taken calculated in (b) increase, decrease, or stay the same? Briefly explain your answer. (1 point)