 # temperature increase

How can one calculate the temperature increase from compressing
a gas into half its space?

That allows you to calculate the temperature of the resulting gas provided you know the pressure. Which you don’t, unless you provide another constraint. There are two approximations often used: one is that the system is isothermal, so that any rise in heat escapes to the surrounding environment and the temperature remains constant. Another is the adiabatic approximation where there is no transfer of heat at all. The real world is usually somewhere in between - some heat is lost to the environment but not all. You can look up the adiabatic formula here:

http://he.daveb.net/phys47/html/latex2html/node84.html

Yeah, do what scr4 said.

It’s been too long since I took Chemistry. Lab sessions were so much fun when the teacher wasn’t looking. sooo…

g = my shorthand for gamma

P1 * V1^g = P2 * V2^g

using the ideal gas law…

nRT1/V1 * V1^g = nRT2/V2 * V2^g

cancel

T1/V1 * V1^g = T2/V2 * V2^g

subtract exponents

T1 * V1^(g-1) = T2 * V2^(g-1)

assuming an ideal gas:

T1 * V1^2/3 = T2 * V2^2/3