What mass of water at must be allowed to come to thermal equilibrium with a
cube of aluminium initially at to lower the temperature of the aluminium
to .
[ 4 marks]

To find the mass of water needed to bring a 1.85 kg cube of aluminum from 150°C to 65.0°C, we can start with the concept of thermal equilibrium where the heat lost by the aluminum will equal the heat gained by the water.

First, we calculate the heat lost by the aluminum using the formula:

where:

Now we plug in the values:

Calculating this gives:

Next, we calculate the heat gained by the water:

where:

Assuming the initial temperature of the water is at room temperature ( ), the change in temperature will be:

Setting (since heat lost equals heat gained):

Now, solving for :

Calculating this gives:

Thus, the mass of water required is approximately 0.085 kg or 85 g to bring the aluminum to the desired temperature.