Question

A piston–cylinder device initially contains steam at 3.5 MPa, superheated by 5°C. Now, steam loses heat to the surroundings and the piston moves down, hitting a set of stops, at which point the cylinder contains saturated liquid water. The cooling continues until the cylinder contains water at 200°C. Determine (a) the initial temperature, (b) the enthalpy change per unit mass of the steam by the time the piston first hits the stops, and (c) the final pressure and the quality (if mixture).

Answer 1

Answer :

(a) The Initial temperature of the steam is 247.557°C

(b) The enthalpy change per unit mass of the steam is -1771 kJ/kg

(c) The final pressure is 1555 kPa, and the liquid vapor mixture contains small mass of vapor.

Explanation :

From the given statements, we know

Initial steam pressure ($P_1$) = 3.5 MPa

Degree of Super heat = 5°C

Saturation Temperature ($T_s_a_t$) = 242.557°C [From Steam Table]

Now, the Initial temperature ($T_1$) of steam is given by-

$T_1$ = $T_s_a_t$ + Degree of Superheat

 = 242.557 + 5 = 247.557°C

(b)To find: The enthalpy change per unit mass of the steam is  

We know enthalpy (h) change is given by

Δh = $h_2$ – $h_1$

From steam Table, properties of the gas at state 1 and state 2  

$h_1$ = 2821.1 kJ/kg

$h_2$ = 1049.7 kJ/kg

On substituting the values, we get

or, Δh = 1049.7 - 2821.1 = -1771 kJ/kg

(c) To Find: The final pressure of the liquid vapor mixture contains small mass of vapor.

We find that the gas at the final position, i.e., at position 3

Final Temperature ($T_3$) = 200°C [Given] ……………………………..(1)

Specific Volume ($v_3$) = Specific Volume ($v_2$) = 0.00123 $m^3$/kg ….....(2)

Using steam table for corresponding values of (1) and (2), we get

Final Pressure $P_3$ = 1555 kPa

Dryness fraction ($x_3$) = 0.0006.