What is the relationship between the volume, pressure, and energy of gases? I know Boyle's and Charles' laws, but I can't figure out how to relate energy.

3 answers

No, no I don't understand what you're saying. Could you please explain?

Is there not a simple formula that relates volume, pressure, and energy? For example, if I had a balloon with hydrogen gas in it, how would I calculate the amount of energy stored by the gas?
Thanks.
E = f/2 N k_b T

N is the number of gas molecules, k_b is Boltzmann's constant:

k_b = 1.38065*10^(-23) J/K

T is the absolute temperature and f is the number of degrees of freedom per molecule.

For a mono-atomic gas like e.g. helium f = 3. This is because an atom can move in three directions. Kinetic energy is 1/m v^2 = 1/2 m (v_x^2 + v_y^2 + v_z^2)

and all three components of the velocity will contribute equally to the internal energy.

In case of hydrogen, there are two additional degrees of freedom. The hydrogen molecule can rotate and you can choose two independent rotation axes orthogonal to the line connecting the two hydrogen atoms. The third possibility of the axis parallel to the molecule doesn't count at room temperatures, because the lowest possible energy above the ground state is so high comnpared to k_b T that this degree of freedom is "frozen". The same is true for the vibrational degrees of freedom at room temperature.

So for hydrogen at room temperature f = 5.