20\frac{kg}{h} of water vapour at 150°C is mixed with some pure cold water at 20°C and the resultant mixture leaves the mixer at 50°C in liquid form. Given the following information, determine the required mass flow rate of the inlet cold water in \frac{kg}{h} to 2 decimal places.
- Specific heat capacity of water is 4.2 \frac{kJ}{kg.K} and it does not change with temperature.
- Specific heat capacity of water vapour is 2.0 \frac{kJ}{kg.K} and it does not change with temperature.
- The latent heat of vaporisation of water is 2258 \frac{kJ}{kg}.
- If required, use 0°C as the reference temperature for your calculations.
- The mixer is adiabatic, i.e. it does not lose any heat to the surrounding.
- The mixer is atmospheric, i.e. it works at constant 1 atm. At this pressure, the boiling point of water is 100°C.
\(m_{cold\ water} =\)