Question

An insulated, rigid vessel is initially empty (evacuated). However, it is connected to a steam line that is maintained at 200 psia and 745 ∘ ∘ F. The valve is opened until the flow into the tank slows and stops (which occurs when the pressure in the tank is equal to the pressure in the steam line), at which point the valve is closed. What is the temperature within the vessel?

Answer 1

Given:

Working Medium= Steam

m1=0, as the system is initially empty

T1=745 F

P1=200 psi

P2=200 psi as the valve is opened until the flow into the tank slows and stops due to pressure equivalency

To Find: T2=?

Assumptions:

Kinetic and Potential Energy is ignored.

The system has no work done and ideal gas is used.

Solution:

We will start the question from basics and try to find answers by using the basic equations, the mass balance and energy balance

As per the mass balance transit equation,

and, as no mass is leaving the system, so m_o will be zero,

so the equation will become

Now according to, Energy balance transit equation

We have ignored Kinetic and potential energy so so (V)² and Z will be zero and as system has no work done so Q-W will be zero as well

Even no mass is moving from the system, so the final equation will be,

Integrating by initial and final stage

But as the system is initially evacuated, so

We need to find Specific Enthalpy from steam table which I did online and results are below, this is for 745F and 200psia

The final temperature using u₂=3249.94 KJ/kg and P₂= 200psia

T2= 745F, same as the temperature of the gas.

I have done best as per my understanding, if you face any doubts then feel free to ask.