A 445 g sample of ice at –58oC is heated until its temperature reaches –29oC. Find the change in heat content of the system.
To find the change in heat content of the system, we need to calculate the heat gained or lost during the temperature change.
First, we need to calculate the heat gained or lost during the phase change. Since the ice is heated, it will undergo a phase change from solid to liquid before reaching the final temperature.
To calculate the heat gained during the phase change, we use the formula:
Q_phase = m * ΔH_fusion
Where:
Q_phase is the heat gained or lost during the phase change
m is the mass of the substance (ice)
ΔH_fusion is the heat of fusion, which is the amount of heat required to change 1 gram of a substance from solid to liquid at its melting point
The heat of fusion for water is 334 J/g.
Q_phase = 445 g * 334 J/g
Q_phase = 148,630 J
Next, we need to calculate the heat gained or lost during the change in temperature. We use the formula:
Q_temp = m * C * ΔT
Where:
Q_temp is the heat gained or lost during the temperature change
m is the mass of the substance (ice)
C is the specific heat capacity of the substance
ΔT is the change in temperature
The specific heat capacity of ice is 2.09 J/g°C.
ΔT = final temperature - initial temperature
ΔT = -29°C - (-58°C)
ΔT = 29°C - 58°C
ΔT = 29°C + 58°C
ΔT = 87°C
Q_temp = 445 g * 2.09 J/g°C * 87°C
Q_temp = 82,206 J
Finally, we can calculate the total change in heat content of the system by adding the heat gained during the phase change and the heat gained during the temperature change:
Change in heat content = Q_phase + Q_temp
Change in heat content = 148,630 J + 82,206 J
Change in heat content = 230,836 J
Therefore, the change in heat content of the system is 230,836 Joules.