Determine the quantity of heat required to convert 1kg of ice at
−20
degrees Celsius to water at 100 degrees Celsius? Specific heat capacities of water and ice water are 2302 J/kgK and 4186 J/kgK respectively
8.0E5J
To determine the quantity of heat required to convert 1kg of ice at -20 degrees Celsius to water at 100 degrees Celsius, we need to consider two steps:
1. Heating the ice from -20 degrees Celsius to 0 degrees Celsius
2. Melting the ice at 0 degrees Celsius to water at 0 degrees Celsius
3. Heating the water from 0 degrees Celsius to 100 degrees Celsius
Step 1: Heating the ice from -20 degrees Celsius to 0 degrees Celsius
The amount of heat required to raise the temperature of a substance can be calculated using the formula:
Q = mcΔT
Where:
Q = heat energy absorbed
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature
For this step, the mass (m) is 1kg, the specific heat capacity (c) is 4186 J/kgK, and the change in temperature (ΔT) is 0 - (-20) = 20 degrees Celsius.
Therefore, the heat energy required to raise the temperature of ice from -20 degrees Celsius to 0 degrees Celsius is:
Q1 = (1kg)(4186 J/kgK)(20 K)
= 83720 J
Step 2: Melting the ice at 0 degrees Celsius to water at 0 degrees Celsius
The heat energy required to melt a substance at its melting point is calculated by:
Q = mL
Where:
Q = heat energy absorbed
m = mass of the substance
L = latent heat of fusion
For this step, the mass (m) is 1kg, and the latent heat of fusion (L) for ice is 334000 J/kg.
Therefore, the heat energy required to melt the ice is:
Q2 = (1kg)(334000 J/kg)
= 334000 J
Step 3: Heating the water from 0 degrees Celsius to 100 degrees Celsius
Use the formula used in step 1 to calculate the heat energy:
Q3 = (1kg)(2302 J/kgK)(100 K)
= 230200 J
Finally, we can calculate the total quantity of heat required by adding up the results of each step:
Total heat energy required = Q1 + Q2 + Q3
= 83720 J + 334000 J + 230200 J
= 647920 J
Therefore, the quantity of heat required to convert 1kg of ice at -20 degrees Celsius to water at 100 degrees Celsius is 647920 Joules.