150g of ice is removed from a freezer at a temperature of -15°C. The ice is left, eventually reaching thermal equilibrium with its surroundings at a temperature of 21°C. If the latent heat of fusion for water is 336 kl/kg, the specific heat capacity of ice is 2100 J/kg.°C, and the specific heat capacity of water is 4200J/kg.°C, how much energy goes into the ice? Where does this energy come from?

It is left in warm air, which gets colder :)

0.15 kg of ice or water, call it m to save typing
heat to warm ice from -15 to 0
Hwarm =m * 2100 * (0 - -15) = m * 2100 (15)
Hmelt = m * 336,000
Hrise = m * 4200 * (21-0)
add them and then use 0.15 kg for m

To find the energy that goes into the ice, we need to calculate two separate quantities: the energy required to raise the temperature of the ice from -15°C to 0°C and the energy required for the phase change (melting) from ice at 0°C to water at 0°C.

First, let's calculate the energy required to raise the temperature of the ice. The specific heat capacity of ice is given as 2100 J/kg.°C, and we have 150g (0.15 kg) of ice. The temperature change is from -15°C to 0°C, so the temperature difference is 15°C:

Energy for temperature increase = mass × specific heat capacity × temperature difference
= 0.15 kg × 2100 J/kg.°C × 15°C
= 4725 J

Next, let's calculate the energy required for the phase change (melting) from ice at 0°C to water at 0°C. The latent heat of fusion for water is given as 336 kJ/kg (or 336,000 J/kg), and we have 150g (0.15 kg) of ice:

Energy for phase change = mass × latent heat of fusion
= 0.15 kg × 336,000 J/kg
= 50,400 J

Now, we can find the total energy that goes into the ice by adding the energy for temperature increase and the energy for phase change:

Total energy = Energy for temperature increase + Energy for phase change
= 4725 J + 50,400 J
= 55,125 J

Therefore, a total of 55,125 J of energy goes into the ice.

As for where this energy comes from, it usually comes from the surroundings. In this case, as the ice is left to reach thermal equilibrium with its surroundings at a temperature of 21°C, the energy most likely comes from the ambient air or objects in the surrounding environment, such as the room temperature or other objects in the freezer. The surrounding environment transfers its energy to the ice, causing it to warm up and eventually melt.