An ice cube tray of negligible mass contains 375 g of ice at -5.00 C. What minimum amount of heat must be added to make all the ice into water?
To find the minimum amount of heat required to make all the ice into water, we need to calculate the heat required to raise the ice's temperature from -5.00°C to its melting point, and then the heat required to melt the ice.
To start, we need to calculate the heat required to raise the ice's temperature using the specific heat formula:
Q = mcΔT
Where:
Q is the heat energy in joules (J)
m is the mass of the ice in kilograms (kg)
c is the specific heat capacity of ice in joules per kilogram per degree Celsius (J/kg°C)
ΔT is the change in temperature in degrees Celsius (°C)
Given:
Mass of ice (m) = 375 g = 375/1000 = 0.375 kg
Specific heat capacity of ice (c) = 2.09 J/g°C
Change in temperature (ΔT) = 0°C - (-5.00°C) = 5.00°C
Plugging in these values into the formula, we have:
Q = (0.375 kg) x (2.09 J/g°C) x (5.00°C)
Q = 3.9375 J
The heat required to raise the temperature of the ice to its melting point is 3.9375 J.
Next, we need to find the heat required to melt the ice using the formula:
Q = mL
Where:
Q is the heat energy in joules (J)
m is the mass of the ice in kilograms (kg)
L is the latent heat of fusion in joules per kilogram (J/kg)
Given:
Mass of ice (m) = 375 g = 375/1000 = 0.375 kg
Latent heat of fusion of ice (L) = 334,000 J/kg
Plugging in these values into the formula, we have:
Q = (0.375 kg) x (334,000 J/kg)
Q = 125,250 J
The heat required to melt the ice is 125,250 J.
To find the minimum amount of heat required to make all the ice into water, we add the two amounts of heat together:
Total heat required = Heat to raise temperature + Heat to melt ice
Total heat required = 3.9375 J + 125,250 J
Total heat required = 125,253.9375 J
Therefore, the minimum amount of heat that must be added to make all the ice into water is approximately 125,253.94 J.