Question

1) A nonconducting tank of negligible heat capacity and 1 m3

volume is connected to
pipeline containing steam at 5 bar and 370℃, filled with steam to a pressure of 5 bar,
and disconnected from the pipeline.
a) If the tank is initially evacuated, how much steam is in the tank at the end of the
filling process, and what is its temperature?
b) If the tank initially contains steam at 1 bar and 150℃, how much steam is in the
tank at the end of the filling process, and what is its temperature?
c) Repeat your calculations of parts a and b if steam behaves like an ideal gas.
d) Repeat your calculations of parts a and b if steam behaves like a van der Waals
fluid

Answer 1

The tank will contain 1 m³ of steam at a temperature of 370℃ if initially evacuated. If the tank initially contains steam at 1 bar and 150℃, the amount of steam in the tank at the end of the filling process can be calculated considering the ideal gas law. The calculations will be the same if steam behaves like an ideal gas, but if it behaves like a van der Waals fluid, the van der Waals equation of state should be used.

Step-by-step explanation:

a) If the tank is initially evacuated:

The tank is connected to a pipeline containing steam at 5 bar and 370℃. When the tank is filled with steam to a pressure of 5 bar, it will contain the same amount of steam as the volume of the tank, which is 1 m³.

The temperature of the steam in the tank will be the same as the temperature of the steam in the pipeline, which is 370℃.

b) If the tank initially contains steam at 1 bar and 150℃:

Since the initial pressure and temperature of the steam in the tank are lower than that of the steam in the pipeline, steam will flow from the pipeline into the tank until the pressures are equal.

The amount of steam in the tank at the end of the filling process can be calculated using the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

Using the given values, we can calculate the number of moles of steam in the tank and then convert it to the corresponding volume.

The temperature of the steam in the tank will be the same as the temperature of the steam in the pipeline, which is 370℃.

c) If steam behaves like an ideal gas:

The calculations for parts a and b will remain the same, as steam is typically approximately treated as an ideal gas in these temperature and pressure ranges.

d) If steam behaves like a van der Waals fluid:

The van der Waals equation of state should be used in the calculations for parts a and b. This equation takes into account the intermolecular forces and the volume occupied by the molecules.

The calculations will involve solving the van der Waals equation for the unknown volume and temperature of the steam in the tank.