Question

A rigid, insulated, empty vessel is to be filled with steam from a steam line at 7 bar and 320°C. Steam flows into the vessel until the pressure in the vessel is 7 bar. At this instant the valve on the charging line is closed.

(a)  What is the temperature of the steam in the vessel at the instant the valve is closed?

(b)  What is the final pressure of the steam in the vessel after it has reached mutual stable equilibrium with the environment at 20° C?

(c)  How much energy is transferred per kilogram of steam as the steam and the environment come to mutual stable equilibrium?

Answer 1

The ideal gas equation is,

(1)

In this particular situation, the volume of the transferred steam and the empty vessel will be the same.

or,      (2)   

(a) Since, the ratio has to remain a constant, any value of and together should satisfy this relation.

Let    , and . Let the temperature at which the instant valve is closed be . Using the relation (2), we get,

  

     

We get,  

(b). Let the final pressure and temperature at which the steam in the vessel reaches equillibrium be and respectievely. Here, .

Hence,

or

(c). Energy will be transferred between the vessel and the enviornment till an equilibrium is attained, that is, when the energy lost by the hot object will be equal to the energy gained by the cold object is equal.

The change in energy is related to the change in temperature by the relation, , where C is the heat capacity or the energy required to raise the temperature of the system by 1 unit of temperature per unit mass. The heat capacity of steam is 1.996 kJ/kgK.

The equillibrium temperature is and the temperature before the equilibrium is . Therefore, .

.

Energy transferred to attain equilibrium per kilogram is 598.8 kJ/kg and the negative sign denotes the outward flow of energy from the vessel.