Question

1. (a) A 0.5 kg sample of ice is in a container of negligible heat capacity open to the atmosphere. Heat Q is supplied at a constant rate H = dQ/dt = 5kW until all the ice has turned to steam. Sketch the process on P-V and P-T diagrams. [2] Assuming an initial temperature of -10 °C and that heat losses are negligible, [4] [4] calculate; (i) the time for all the ice to reach its melting point. (ii) the time taken for all the ice to change phase from solid to liquid. (iii) the time for all the liquid to reach the boiling point. [2] (iv) the time taken for all the liquid to turn to steam. [2] (v) the total energy added to the sample. [2] (b) Make a labelled sketch of the temperature as a function of time.​

Answer 1

To sketch the process on a P-V diagram, follow the steps of the ice melting and boiling process. Calculate the time for each phase change and the total energy added to the sample. On a temperature vs. time graph, the temperature will rise linearly, remain constant during phase changes, and increase faster during the boiling phase.

To sketch the process on a P-V (pressure-volume) diagram, we can consider the following steps:

1. At -10°C, the ice is in the solid phase and occupies a certain volume.
2. As heat is supplied, the ice temperature rises linearly until it reaches its melting point at 0°C. During this phase, the volume remains constant.
3. After reaching its melting point, the ice begins to melt and transition to the liquid phase. The volume still remains constant.
4. Once all the ice has melted, the liquid water temperature rises linearly until it reaches its boiling point at 100°C, and the volume remains constant.
5. At the boiling point, the liquid water starts to boil and changes to the gaseous phase, still with a constant volume.

To sketch the process on a P-T (pressure-temperature) diagram, we can represent the same steps described above but with temperature on the y-axis instead of volume.

(i) The time for all the ice to reach its melting point can be calculated by dividing the energy required to raise its temperature from -10°C to 0°C by the rate at which heat is supplied.

(ii) The time taken for all the ice to change phase from solid to liquid is determined by dividing the heat of fusion by the rate at which heat is supplied.

(iii) The time for all the liquid to reach the boiling point can be calculated by dividing the energy required to raise its temperature from 0°C to 100°C by the rate at which heat is supplied.

(iv) The time taken for all the liquid to turn to steam is determined by dividing the heat of vaporization by the rate at which heat is supplied.

(v) The total energy added to the sample can be calculated by summing the energy for each phase change and the energy used to raise the temperature of the sample.

In a labeled sketch of the temperature as a function of time, the temperature will rise linearly until it reaches 0°C, remain constant at 0°C during the melting phase, rise linearly again until it reaches 100°C, and then remain constant at 100°C during the boiling phase.