Plan your route before writing. Use equations, diagrams, units, and a clear final justification where needed.
On a hot day, the air temperature in a sealed, well-insulated bedroom is 24 °C. To cool the room down, a person takes a solid block of ice from the freezer, places it directly in front of an electric fan, and closes the door.
The room measures 5.0 m × 4.0 m × 2.5 m.
The ice block measures 0.25 m × 0.20 m × 0.10 m and is initially at 0 °C.
Use the following data:
density of air = 1.2 kg m^-3
specific heat capacity of air = 1000 J kg^-1 K^-1
density of ice = 920 kg m^-3
specific heat capacity of water = 4200 J kg^-1 K^-1
specific latent heat of fusion of ice = 3.3 × 10^5 J kg^-1
(a)
2 marks
Calculate the mass of air in the room.
(b)
2 marks
Calculate the mass of the ice block.
(c)
3 marks
The ice melts completely and the meltwater then warms up to the air temperature. Calculate the total energy absorbed by the ice and meltwater as it melts at 0 °C and then warms to 24 °C.
(d)
2 marks
Assume the room is perfectly sealed and insulated, and that all of the energy absorbed by the ice and meltwater is taken from the air. Calculate the drop in temperature of the air in the room.
(e)
2 marks
The fan's motor is rated at 60 W. Assume that all of the electrical energy supplied to the motor is eventually transferred to the air in the room as thermal energy. It takes 2.0 hours for the ice to melt completely. Calculate the temperature rise of the air caused by the motor running over this time.
(f)
3 marks
Using your answers and the idea of internal energy, evaluate the claim that placing ice in front of a fan is an effective way to cool a sealed room. In your answer, explain why running the fan alone (with no ice) would warm the room, and why a fan can still make a person feel cooler.
