# If a gas in a pipe is travelling from a large cross sectional area to a smaller cross sectional area, will it cool down?

So in a problem like the one in the link below:

Velocity increases, so pressure must decrease, thus the pressure at the small part of the pipe will be smaller (based on an energy balance using the bernoulli equation assuming no mechanical or thermal energy)

Now, if we look at the ideal gas law:

PV=nRT (where V is volume per unit time and n is moles per unit time)

V, n, and R are do not change from the large part to the small part. However, the pressure decreases, so we would need to see a decrease in temperature?

So would this imply that in any situation with a nozzle like the one in the video that the fluid on the small side of the nozzle would always be colder than the one on the side with the large cross sectional area?

Intuitively...it does not make a lot of sense, but the math seems to work out, please let me know what you think!