Question

Turbines in electric power stations are driven by high pressure steam produced by boiling water in a boiler. The pressure in the boiler could be as high as 300 atm. This high pressure steam could explode in a disastrous way if there was a fault in the boiler. Before use, boilers are tested by filling them with water, and pressurising the water to, for example, 300 atm. Let's guess that this reduces the volume of the water to 98.5% of its initial volume. Draw a PV diagram of this process – doesn't need to be to scale. Assume that the PV curve is a straight line, and so you can easily figure out the average pressure during this process. Calculate the work done on 1 litre of water. Explain why it has this small value, even though the pressure is very large. Explain why this is a safe way of testing boilers.

Answer 1

Assuming the PV curve to be a straight line, it can be drawn as

,

where stands for "initial" and stands for "final". For example, is the initial volume and is the final one. Same thing follows for the pressure .

Now, the equation of the straight line should be

Hence the work done in this process should be

This could be done more easily if we consider the average pressure

and calculate the work done as

The work done is quite small even if the final pressure is so high. This is because the change in the volume is so small:

.

This is a safe way of testing boilers. Because in this way, any deviation from the control settings (deviation from the straight line) will be detected.