Why don't we burn our hands when using a garden water hose?

Question

When I connected the garden water pipes to the main water grid by closing the spill valves (used to drain the water out of the pipes to prevent water freezing in there during winter), it struck me that there is no noticeable temperature increase at the (now closed) and pressurized water nozzles in the garden. So, the pipes were full of air, I put 6 bar water pressure on the system (5 bar overpressure), the temperature of the compressed air that is now being pushed at the nozzle ends should then increase from an initial, say $10^{\circ}\text{ C}$ to $\left[6^{2/7}(273 + 10) - 273\right] ^{\circ}\text{ C} \approx 200^{\circ}\text{ C}$.

Now, you could say that the water will cool things down, and the whole system has a large heat capacity anyway and there is significant heat conduction to the cold metal pipes and the water. But we typically don't notice anything when using a small water hose either. People don't regularly burn their hands after connecting the hose to the water mains, turning the water tap and then holding the hose at the end filled with compressed air.

Also, why don't we see water in a pressurized hose boil for a while? At $200^{\circ}\text{ C}$ the vapor pressure is about 15.5 bar which greatly exceeds the 6 bar pressure in a pressurized hose.

Answer 1

The heat capacity of air is quite tiny and you have a lot of pipe around it!

When you pressurize the air, you do indeed raise its temperature. However, air has a very small heat capacity per volume, so the heat energy associated with that increase in temperature is pretty small. Meanwhile, the air is surrounded by lots of pipe material, copper or rubber, which has a much higher heat capacity. The system equalizes at a temperature much closer to room temperature when you do this.

You could see some vaporization of the water for a few moments, though you might not think of it as a "boil" because you wouldn't have any bubbling. However, that vaporization will rapidly decrease the temperature to below the boiling point of water. Water has an astonishingly high heat capacity. It's also highly conductive of heat so once the heat gets to the water, it will spread that heat further up stream rapidly.

So basically, the mathematical rule you used to calculate the temperature assumed an adiabatic process. However, in the pipe system you describe, that adiabatic assumption isn't reliable.