Question

At time t = 0, a vessel contains a mixture of 18 kg of water and an unknown mass of ice in equilibrium at 0°C. The temperature of the mixture is measured over a period of an hour, with the following results: During the first 47 min, the mixture remains at 0°C; from 47 min to 60 min, the temperature increases steadily from 0°C to 2.0°C. Neglecting the heat capacity of the vessel, determine the mass of ice that was initially placed in the vessel. Assume a constant power input to the container.

Answer 1

To determine the mass of ice initially placed in the vessel, we can use the principle of heat transfer. We know that during the first 47 minutes, the mixture remains at 0°C, and from 47 minutes to 60 minutes, the temperature increases from 0°C to 2.0°C. By calculating the heat gained by the ice during this phase and comparing it to the total heat gained during the hour, we find the mass of the ice initially placed in the vessel to be 2 kg.

Step-by-step explanation:

To determine the mass of ice initially placed in the vessel, we can use the principle of heat transfer. We know that during the first 47 minutes, the mixture remains at 0°C, and from 47 minutes to 60 minutes, the temperature increases from 0°C to 2.0°C.

Let's consider the heat gained by the ice during the second phase when the temperature increases. The heat gained by the ice can be calculated using the equation:

Q = mLf, where Q is the heat gained, m is the mass of ice, and Lf is the latent heat of fusion for ice.

Since the temperature change is from 0°C to 2.0°C, we can calculate the heat gained by the ice during this phase:

Q = m(2.0°C - 0°C) = 2m

Now, let's calculate the heat gained by the ice during the entire hour:

Q = mLf

Since the heat gained by the ice during the second phase is 2m, and the total heat gained is mLf, we have:

mLf = 2m

Simplifying the equation, we find:

Lf = 2

Therefore, the mass of ice initially placed in the vessel is 2 kg.