The heat of vaporization of water is 40 kJ mol-1 at 100oC. What percentage of the heat supplied to vaporize the water can be converted into work if the water is vaporized at 100 degrees C against a constant pressure of 1 atm?
To determine the percentage of heat supplied to vaporize the water that can be converted into work, we need to understand the concept of Gibbs Free Energy (ΔG) and the equation for work done (W) by a system.
The Gibbs Free Energy (ΔG) is a measure of the available work in a system, and it can be calculated using the equation:
ΔG = ΔH - TΔS
Where:
- ΔG is the Gibbs Free Energy change
- ΔH is the enthalpy change (in this case, the heat of vaporization, given as 40 kJ mol-1)
- T is the temperature in Kelvin
- ΔS is the entropy change
At a constant pressure, the work done by a system (W) is given by the equation:
W = - ΔG
Since we want to find the percentage of heat supplied that can be converted into work, we can use the following equation:
Percentage of heat converted into work = (W / Q) * 100
Where:
- W is the work done by the system
- Q is the heat supplied
To solve this problem, we need to consider that the heat supplied (Q) is equivalent to the enthalpy change (ΔH) during the process of vaporization. We also need to know the value of temperature (T) to calculate the Gibbs Free Energy change (ΔG).
Given that the water is vaporized at 100 degrees C against a constant pressure of 1 atm, we need to convert the temperature to Kelvin.
T (in Kelvin) = 100 + 273.15 = 373.15 K
Now we can calculate the Gibbs Free Energy change (ΔG) using the equation:
ΔG = ΔH - TΔS
In this case, since the pressure is constant, the entropy change (ΔS) is zero. Therefore:
ΔG = ΔH = 40 kJ mol-1
Next, we can calculate the work done (W) by the system:
W = - ΔG = - 40 kJ mol-1
Finally, we can calculate the percentage of heat converted into work:
Percentage of heat converted into work = (W / Q) * 100
Since Q (heat supplied) is equal to the enthalpy change (ΔH) of 40 kJ mol-1, we have:
Percentage of heat converted into work = (-40 kJ mol-1 / 40 kJ mol-1) * 100 = -100%
Therefore, in this case, the percentage of heat supplied to vaporize the water that can be converted into work is 100%. Note that the negative sign indicates that work is done on the system, rather than by the system.