# Why temperature increases with increase in volume?

If We heat an ideal gas, its temperature rises and it's molecule becomes energetic hence they move more and more away from equilibrium position.

But when we increse the volume of gas , why does its temperature increases? . Increasing volume does not leads to increse in avg kinetic energy per molecules(temperature)

I cannot relate it with Charles law , so pls explain

• Who told you that it would? Feb 15, 2022 at 14:10
• If you heat a gas it will expand, but if you expand a gas it doesn’t heat, it cools. Feb 15, 2022 at 14:11
• You don't. The causality is heat --> volume increase. Feb 15, 2022 at 14:58
• It means that , Charles law is one way
– user325981
Feb 15, 2022 at 15:11

Charles's law states:

When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion.

and the key point here is that the pressure must remain constant. We can see this from the ideal gas equation of state:

$$PV = RT$$

If we rearrange this to:

$$V = \left(\frac{R}{P}\right) ~ T$$

then we get $$V$$ proportional to $$T$$ only if $$R/P$$ is a constant i.e. only if the pressure $$P$$ is constant.

The problem is that if we just increase the volume without doing anything else the pressure will fall. To keep the pressure constant we have to add heat to the gas, and it's the heat we have to add to the gas that makes the temperature increase. Conversely, if we reduce the volume then we have to take heat out to keep the pressure constant, and this is why the temperature falls.

So when you read that Charles's law says $$V \propto T$$ this can be a little misleading because you need to remember that this only applies if you also add or remove heat to keep the pressure constant.

If We heat an ideal gas, its temperature rises and it's molecule becomes energetic hence they move more and more away from equilibrium position.

Its temperature will not necessarily rise. It depends on the process.

If the gas is in thermal contact with a constant temperature surroundings (thermal reservoir) and the external pressure is gradually reduced such that the product of the gas pressure and volume is constant, the expansion will occur isothermally (at constant temperature).

But when we increase the volume of gas , why does its temperature increases? Increasing volume does not leads to increase in average kinetic energy per molecules(temperature).

Again, an increase in volume does not necessarily mean an increase in temperature because it depends on the process, as stated above.

I cannot relate it with Charles law , so pls explain

Now, if Charles' law applies, we know something about the process, or at least the initial and final states. To explain:

Charles' law states that the volume of a gas equals a constant value multiplied by its temperature in degrees Kelvin. It follows from the ideal gas law

$$pV=nRT$$

$$V=\frac{nRT}{p}$$

for a closed system, the number of moles $$n=$$ constant and $$R$$ is the universal gas constant . Thus if $$V$$ equals a constant times $$T$$, per Charles' law the pressure $$p$$ must be constant. Then, since from the ideal gas law

$$\frac{p_{1}V{_1}}{T_{1}}=\frac{p_{2}V{_2}}{T_{2}}$$

If $$p_{1}=p_2$$

$$\frac{V{_1}}{T_{1}}=\frac{V{_2}}{T_{2}}$$

So in the case of a constant pressure process, if $$V_{2}\gt V_1$$ then we must have $$T_{2}\gt T_1$$.

Hope this helps.

• Mr. Bob , would you pls answer my latest question?
– user325981
Feb 16, 2022 at 7:15

In order to get the gas volume to increase at constant pressure, you need to add heat, which raises the temperature (average kinetic energy) of the gas.