# Pressure increase in a closed system

1. Oct 17, 2013

### DarkF1ame

Hello All,

I work in the refrigeration industry, and I'm trying to put a hard number on a hypothetical situation. The situation is a lapse in SOP and liquid gets trapped in a line. For this hypothetical situation the line is 100% full. What would the increase in pressure be per degree?

I know that the density (g/cm3) goes down as temperature is increased. So with a fixed mass, the cm3 number must go up to lower the overall density, but since the scenario is 100% full, my brain tells me that energy is getting transmitted into the pipe walls as pressure since it can't physically expand any more. What I can't figure out is how to enumerate that pressure gain.

Any help would be greatly appreciated.

For this example, the trapped liquid in the pipe is water.

Thanks,

Scott

2. Oct 17, 2013

### Staff: Mentor

If the pipe is rigid so that it doesn't expand, then first you calculate how much the water would expand if it were not constrained (volumetric strain). This is determined by its coefficient of thermal volume expansion. Then you calculate how much pressure would be required to remove that same amount of volumetric strain. This would be determined by the bulk modulus of the fluid.

Chet