The internal energy of an ideal gas is a function only of temperature. We know this because, if you have a real gas at low pressure in half of a rigid container and vacuum in the other half, and you break the seal, after the system has re-equilibrated at a lower pressure, the temperature does not change. This shows that the internal energy does not depend on pressure. A real gas in the limit of low pressures is what we refer to as an ideal gas.Lairix said:I don't understand how Delta(U) = Cvdelta(T) is always true for Ideal Gases...Shouldn't this only be true for constant volume processes? Yet it seems to be used even when a gas is expanding or being compressed...
Any ideas...Thanks in advance.
The equation for the change in internal energy (ΔU) for ideal gases is ΔU = CvΔT, where Cv is the heat capacity at constant volume and ΔT is the change in temperature.
The symbol "Cv" represents the heat capacity at constant volume, which is the amount of heat required to raise the temperature of a substance by one degree while keeping its volume constant.
No, this equation only applies to ideal gases, which are hypothetical gases that follow the ideal gas law under all conditions.
This equation is derived from the first law of thermodynamics, which states that the change in internal energy is equal to the heat added to the system minus the work done by the system. For ideal gases, the work done is zero, so the change in internal energy is equal to the heat added, which is represented by CvΔT.
The units for Cv depend on the units used for temperature and energy, but they are typically in joules per mole per Kelvin (J/molK). The units for ΔT are in Kelvin (K).