Question

A piston–cylinder device initially contains 50 L of liquid water at 40°C and 200 kPa.
Heat is transferred to the water at constant pressure until the entire liquid is vaporized.
(a) What is the mass of the water?
(b) What is the final temperature?
(c) Determine the total enthalpy change.

Answer 1

Final Answer : (a) 49.6 kg
(b) 120.21°C
(c) 125,922 KJ

Assumptions :
1) At 40°C, initial state is saturated apart from compressed liquid state.
2) There is no/ negligible loss of heat to surroundings.


Analysis :
1) At 40°C,
From Saturated water- Temperature Table-1 ,

Specific volume of saturated liquid,
$v_f = 0.001008 m^3 /kg$

Volume of Container, V = 0.05m^3
Then,
Mass of water, M = Volume of container / Specific Volume
$M = \frac{V}{v_f} = \frac{0.05}{0.001008} \\ = > M = 49.6 kg$

2) After entire liquid is vaporised, Final Temperature is equal to saturated temperature at 200kPa , (From Table -2)
$T_f = T_{sat.@ 200kPa } = 120.21 °C$

3) Enthalpy from Table -1,
Saturated liquid , h_1 ,
Saturated vapour at 200kPa (sat) , h-2
$h_{1}= 167.53 KJ/kg \\ h_2 = 2706.3 KJ/ kg \\ \Delta H = m(h_2-h_1) \\ => 49.6 (2706.3-167.53) \\ => 125,922KJ (approx.)$


Enthapy Change = 125,922 KJ (approx.)

Answer 2

Why  we use  temperature  and pressure not  take at a  same  time   to  find vf of liquid