# Entropy of gas

Can anyone please answer this question? I have read that increased temperature increases entropy and increased pressure decreases entropy ,for a gas.And vice versa.decreased temperature decreases entropy and decreased pressure increases entropy.Can any one please tell me for a gas under pressure that is compressed further does the increase in temperature increase the entropy more than the increase in pressure reduces it and for a gas under pressure that expands does the decrease in temperature decrease the entropy more than the decrease in pressure increases it.In other words does temperature trump pressure or vice versa.
And does it make any difference whether the gas (which is already under pressure) is compressed or expanded?
Thanx, RanCam

phyzguy
Try looking at the Sackur-Tetrode equation, which gives an expression for the entropy of an ideal gas. That, together with the ideal gas law (PV = N kT) should allow you to express the entropy in any terms you want.

Chestermiller
Mentor
Can anyone please answer this question? I have read that increased temperature increases entropy and increased pressure decreases entropy ,for a gas.And vice versa.decreased temperature decreases entropy and decreased pressure increases entropy.Can any one please tell me for a gas under pressure that is compressed further does the increase in temperature increase the entropy more than the increase in pressure reduces it and for a gas under pressure that expands does the decrease in temperature decrease the entropy more than the decrease in pressure increases it.In other words does temperature trump pressure or vice versa.
And does it make any difference whether the gas (which is already under pressure) is compressed or expanded?
Thanx, RanCam
If the compression or expansion is done adiabatically and reversibly, the entropy remains constant. If the compression or expansion is done adiabatically and irreversibly, the entropy increases.

In general, for an ideal gas, $$dS=nC_p\frac{dT}{T}-nR\frac{dP}{P}$$

If the compression or expansion is done adiabatically and reversibly, the entropy remains constant. If the compression or expansion is done adiabatically and irreversibly, the entropy increases.

In general, for an ideal gas, $$dS=nC_p\frac{dT}{T}-nR\frac{dP}{P}$$

Could you elaborate on how this was obtained? Just the first step or two. I will try the rest.

Chestermiller
Mentor
Could you elaborate on how this was obtained? Just the first step or two. I will try the rest.
For a change between two closely neighboring equilibrium states of an ideal gas, the changes in enthalpy, entropy, and volume are related by
$$dH=TdS+VdP=nC_pdT$$
This is the first step.