1mole of liquid water at 25 c and 1 atm forms 1 mole of steam at 100 c and 1 atm. the molar heat capacity of water 373 k is 40.79kj/mol and the molar heat capacity of water is 75.3 J. assume ideal gas behavior for steam. Calculate delta U, delta H and delta S
To calculate delta U (change in internal energy), delta H (change in enthalpy), and delta S (change in entropy) for the given process, we need to use the following equations:
1. Delta U = n*Cv*(T2 - T1)
2. Delta H = n*Cp*(T2 - T1)
3. Delta S = n*Cp*ln(T2/T1)
Where:
- Delta U is the change in internal energy
- Delta H is the change in enthalpy
- Delta S is the change in entropy
- n refers to the number of moles of water (which is 1 mole in this case)
- Cv is the molar heat capacity at constant volume
- Cp is the molar heat capacity at constant pressure
- T1 is the initial temperature (25°C)
- T2 is the final temperature (100°C)
Given values:
- Cv = 40.79 kJ/mol
- Cp = 75.3 J/mol
- T1 = 25°C = 298 K
- T2 = 100°C = 373 K
Let's calculate each value step-by-step:
1. Delta U:
Delta U = 1 * 40.79 kJ/mol * (373 K - 298 K)
= 1 * 40.79 kJ/mol * 75 K
= 3066.75 kJ
2. Delta H:
Delta H = 1 * 75.3 J/mol * (373 K - 298 K)
= 1 * 75.3 J/mol * 75 K
= 5647.5 J
3. Delta S:
Delta S = 1 * 75.3 J/mol * ln(373 K / 298 K)
= 1 * 75.3 J/mol * ln(1.25)
≈ 28.05 J/K
Therefore, the calculated values are:
- Delta U = 3066.75 kJ
- Delta H = 5647.5 J
- Delta S ≈ 28.05 J/K