Temperature Changes with Volume Increase: Charles Law

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Charles' Law states that a gas expands and increases in volume when heated, but the relationship between volume increase and temperature rise depends on the system. It is a specific case of the ideal gas law, represented by the equation pV=nRT, which assumes constant internal energy and applies to isothermal processes. In isobaric processes, where pressure remains constant, an increase in volume indicates that the gas is doing work on its surroundings. For an ideal gas, potential energy between particles is negligible, leading to the equation U= (3/2)nRT for monoatomic gases. Consequently, the change in internal energy (ΔU) is related to temperature change (ΔT) and work done (w). If no heat is exchanged with the surroundings, the temperature will decrease. In cases where external pressure is zero, the gas can expand without doing work, resulting in constant temperature.
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Charles Law says that a gas will expand (increase its volume) as it is heated. Is it also true therefore that the temperature of a gas will rise if it's volume increases somehow?
 
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It depends on the system.

Charles' law is a spesific case of the ideal gas law,

pV=nRT

In this equation, internal energy is held constant, meaning it applies for isothermal processes. In Charles' law the pressure and amount of gas is kept constant.

The following discussion is valid when the gas expands against a uniform external pressure.

If you have an isobaric process (constant pressure) where the volume increases, it means that the gas is doing work on the surroundings. In an ideal gas, there is no potential energy between particles, so

U= \sum E_k + 0=\frac{3}{2}nRT

for a monoatomic gas. From there we get that

\Delta U=\frac{3}{2}nR\Delta T=q-w

If there is no heat from the surroundings, the temperature will sink.

In the special case when the external pressure is zero, the gas expands without doing work and the temperature is constant.
 
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