A 150g iron ball is dropped into a cavity in a block of ice. The cavity is then found to contain 21g of water. Calculate the heat of fusion of ice.
To calculate the heat of fusion of ice, we need to use the principle of conservation of energy. The heat gained by the ice and water is equal to the heat lost by the iron ball.
The equation we will use is:
Heat gained by water + Heat gained by ice = Heat lost by iron ball
The heat gained by water can be calculated using the equation:
Q = m x c x ΔT
Where:
Q is the heat gained by water
m is the mass of water
c is the specific heat capacity of water
ΔT is the change in temperature
In this case, the mass of water is 21g and the change in temperature is the heat of fusion of ice, which is what we are trying to find.
The heat gained by ice can be calculated using the equation:
Q = m x ΔH
Where:
Q is the heat gained by ice
m is the mass of ice
ΔH is the heat of fusion of ice, which is what we are trying to find.
The heat lost by the iron ball can be calculated using the equation:
Q = m x c x ΔT
Where:
Q is the heat lost by the iron ball
m is the mass of the iron ball
c is the specific heat capacity of iron
ΔT is the change in temperature. In this case, the iron ball starts at a higher temperature and cools down to the freezing point of water.
By setting up and solving the three equations, we can determine the value of ΔH, which represents the heat of fusion of ice.