Question

A rigid tank with volume Vtank=20 liter is maintained at T1=300 C and initially contain m1=0.08 kg of water as shown in the figure. At some time, a valve is opened allowing Vin=2 liters of waters at Tin=20 C and Pin=20.0 MPa to enter the tank. The valve is shut and eventually all of the water in the tank comes to T2=300 C.

a)Locate state 1 and state in, the states of the water initially in the tank and the water added to the tank, respectively, on a sketch of a T-v diagram. Indicate on your diagram what two properties define each state as well as lines of constant pressures (isobars), lines of constant specific volume (isochors) and/or lines of constant temperatures (isotherms)).

b)What is the initial pressure in the tank (MPa)?

c)What is the mass of the water added to the tank (kg)?

d)Locate state 2, the final state of the water in the tank, on the T-v diagram from (a).

e) What is the final pressure in the tank (MPa)?

f) Explain how it is possible for the temperature of the water in the tank to remain constant at 3000C after adding water with much lower temperature ( 20oC ) to the tank.

g)On a P-v diagram overlay initial state and final state of water in the tank. Indicate on your diagram what two properties define each states and draw isotherms.

Answer 1

Discharging a Tank Containing Water and Steam The rigid tank, shown below, contains 20 L of liquid water and 45 L of water vapor inequilibrium at 200oC. When the valve in the drain line is opened slightly, liquid water flows slowly out of the tank at a constant rate. Heat transfer into the tank keeps the temperature within the tank uniform andconstant.

Consider for example the T-v duagram for water as shown below: The shaded zone in the diagram indicates the region that can be represented by the Ideal Gas equation to an error of less than 1%. Note that at the critical point the error is 330%. For b and c From the T-v diagram we determine that state (2) is in the superheated region, thus we use the superheated steam tables to determine that v2 = v200kPa,300°C = 1.3162 m3/kg. Thus V2 = m,v2 = (0,5kg).(1.3162 m3/kg) = 0.658 m3 (658 liters) For d Locate state 2, the final state of the water in the tank, on the T-v diagram from (a) lie on the critical point. For e) What is the final pressure in the tank (MPa)- 22MPa as shown in the T-v diagram.