2kg water vapour 100degrees is condensed to water at 40degrees. The quantity of heat required?
mass * [heat of vaporization + (specific heat * temp change)]
No
To determine the quantity of heat required to condense 2 kg of water vapor from 100 degrees Celsius to water at 40 degrees Celsius, we need to consider two steps:
Step 1: Cooling to 100 °C
First, we need to cool the water vapor from 100 degrees Celsius to its boiling point, which is 100 degrees Celsius. The specific heat capacity of water vapor at constant pressure is approximately 1.996 J/g°C.
The formula to calculate the heat required for this step is:
Q = m * c * ΔT
where:
Q = Heat (in Joules)
m = Mass of the substance (in grams)
c = Specific heat capacity (in J/g°C)
ΔT = Change in temperature (in °C)
So, for this step, the calculation will be:
Q1 = (2,000 g) * (1.996 J/g°C) * (100°C - 100°C)
Q1 = 0 Joules
Step 2: Condensation to 40 °C
Next, we need to condense the water vapor to water at 40 degrees Celsius. The heat of condensation for water is approximately 2260 J/g.
The formula to calculate the heat required for this step is:
Q = m * h
where:
Q = Heat (in Joules)
m = Mass of the substance (in grams)
h = Heat of condensation (in J/g)
So, for this step, the calculation will be:
Q2 = (2,000 g) * (2260 J/g)
Q2 = 4,520,000 Joules
Total Heat Required:
To determine the total heat required, we add the heat from both steps:
Total Heat = Q1 + Q2
Total Heat = 0 Joules + 4,520,000 Joules
Total Heat = 4,520,000 Joules
Therefore, the total quantity of heat required to condense 2 kg of water vapor from 100 degrees Celsius to water at 40 degrees Celsius is 4,520,000 Joules.