A 0.106 kg ice cube is taken out of a freezer with temperature -16°C. It is then added to a glass of water with mass 0.25 kg. The water initially has a temperature of 24.2 °C. Assume no heat is added or lost to the surroundings.
Calculate the amount heat required to completely melt the ice when it starts at -16°C. (Assume the specific heat of ice is 2100 J/kg*°C and the latent heat of fusion of ice is 333,700 J/kg.)
To calculate the amount of heat required to completely melt the ice, we need to consider two steps:
1. Raising the temperature of the ice from -16°C to 0°C.
2. Melting the ice at 0°C.
Step 1: Raising the temperature of the ice
The formula to calculate the heat required to raise the temperature of a substance is given by: Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.
In this case, the mass of the ice is 0.106 kg, the specific heat of ice is 2100 J/kg*°C, and the change in temperature is 0 - (-16) = 16°C. Plugging these values into the formula, we get:
Q1 = (0.106 kg) * (2100 J/kg*°C) * (16°C) = 35,136 J
Step 2: Melting the ice
The formula to calculate the heat required to melt a substance is given by: Q = mL, where Q is the heat energy, m is the mass, and L is the latent heat of fusion.
In this case, the mass of the ice is still 0.106 kg and the latent heat of fusion of ice is 333,700 J/kg. Plugging these values into the formula, we get:
Q2 = (0.106 kg) * (333,700 J/kg) = 35,414.2 J
Adding the heat required in step 1 and step 2 gives us the total heat required to completely melt the ice:
Total heat = Q1 + Q2 = 35,136 J + 35,414.2 J = 70,550.2 J
Therefore, the amount of heat required to completely melt the ice starting at -16°C is approximately 70,550.2 J.