How Is Internal Energy Affected in the Water to Steam Conversion at 100°C?

[zorro]

Homework Statement

Calculate the increase in internal energy of 1 kg of water at 100 degrees Celsius when it is converted into steam at the same temperature and at 1atm. The density of water and steam are 1000kg/m³ and 0.6kg/m³ resp. The latent heat of vaporisation of water is 2.25 x 10⁶ J/kg

The Attempt at a Solution

The heat given to convert 1 kg of water to steam is 2.25 x 10⁶ J.
I don't understand whether work is done by the system or on the system in increasing its volume.
The work done (by or on) the system is given by
W=nRTln(V₂/V₁) as the temperature remains same.
On adding both the values I got a wrong answer.
The correct answer is 2.08 x 10⁶ J.

Please explain.

 

[rl.bhat]

Heat added to the system from the environment Q = 2.25x10^6.
Volume if 1 kg of water = 10^-3 m^3
Volume if 1 kg of steam = 1/0.6 = 1.667 m^3
Work done by the system on the environment W = p(Vv - Vl) = 1.013x10^5(1.667 - 0.001)= 168 765.8 Joules.
Hence the increase in internal energy of 1 kg of water at 100 degrees Celsius = Q - W