Two kilograms of water fill this pistoncylinder device which

Two kilograms of water fill this piston-cylinder device which is arranged to maintain a pressure of 400 kPa. The initial quality of the water is 75 %. It is then heated until the water temperature is 200 oC. What is the total amount of heat (in kJ) required for this process?

Solution

m = 2 kg

P₁ = 400 kPa

X₁ = 0.75

T2 = 200 C

Since this is constant pressure

Q = H₂-H₁

Find T sat when P = 400 kPa

T_sat = 143.61 ºC

H_f= 604.66 kJ/kg

H_g = 2738.1 kJ/kg

H₁ = h_f + x(hg-hf ) =604.66 + 0.75x (2738.1-604.66) = 2204.74 kJ/kg

H₁ =2204.74 kJ/kg

Enthalpy at 400 kPa and :

H₂ = 2860.9 kJ/kg

q = H₂-H₁ = 2860.9-2204.74 = 656.16 kJ/kg

m = 2 kg then

Q = 656.16 kJ/Kg x 2 = 1312.32 kJ

Q = 1312.32 kJ