Question

When 3.00g of water at 100°C changes from the liquid to the gas phase at standard atmospheric pressure, its change in volume is 2.45×10−3m3. The latent heat of vaporisation of water is 2260 kJ/kg.
How much heat must be added to vaporize the water?
How much work is done by the water against the atmosphere in its expansion?
What is the change in the internal energy of the water?

Answer 1

1) The amount of heat needed to change water into vapour can be obtained as

$\Delta Q = Lm = 2.260\cdot10^6\,\mathrm{J/kg}\cdot3\cdot10^{-3}\,\mathrm{kg} = 6780\,\mathrm{J}.$

2) The work done by water is $A=P\Delta V = 1.01\cdot10^5\,\text{Pa}\cdot2.45\cdot10^{-3}\,\mathrm{m^{-3}} = 247.45\,\mathrm{J}.$

3) The change of internal will be $\Delta U = \Delta Q - A = 6780\,\mathrm{J} - 247.45\,\mathrm{J} \approx 6532.6\,\mathrm{J}.$