Question

Calculate the increase in internal energy of 1 kg of water at 100°C when it is converted into steam at the same temperature and at 1 atm (100 kPa). The density of water and steam are 1000 kg m^-3 and 0.6 kg m^-3 respectively. The latent heat of vaporization of water = 2.25 × 10⁶ J kg⁻¹

Answer 1

Mass and density of water and steam is provided so from the given data calculate the increase in volume. Pressure term is given so by using pressure volume relationship calculate the work done by the system. Change in internal energy can be calculated using heat and work relation.

The volume of 1 kg of water

= 1/100 m³ and of 1 kg steam = 1/0.6 m³

The increase in volume

The work done by the system is

pΔV (100kPa) (1.7m³ ) 1.7 x 105 J.

The heat given to convert 1 kg of water into steam

= 2.25 x 10 J

The change in internal energy is

ΔU = ΔQ - ΔW = 2.25 x 10⁶ J- 1.7 x 10⁵ J = 2.08 x 10⁶