# The heat capacity of an ideal gas.

• corr0105
In summary, for an ideal gas, the heat capacity CV is independent of volume if ∂U/∂V=0. This means that the change in internal energy is not affected by a change in volume, and therefore the heat capacity only depends on the changing temperature, as represented by the expression CV=∂U/∂T (with v held constant). This relationship can also be derived using Maxwell Relations, but it is not applicable to this specific question as volume is not a function of temperature.
corr0105
The question states: For an ideal gas ∂U/∂V=0. Show that this implies the heat capacity $$_{}C$$V of an ideal gas is independent of volume.

I can't wrap my mind around how I could answer this question besides just stating the obvious. The expression for heat capacity is:
$$_{}C$$V=∂U/∂T (with v held constant)
The subscript V means that volume must be held constant and that heat capacity is only dependent only upon a changing temperature.

The chapter of my thermodynmaics book that this homework problem comes from is about Maxwell Relations, if that helps at all. However, all that helped me do was derive the fact that ∂U/∂V=0 but not actually answer the question.

Any help would be WONDERFUL! thanks so much! :)

Can one use

CV=∂U/∂T = (∂U/∂V)(∂V/∂T)?

I guess I'm not sure how exactly that works, but that would just make the heat capacity 0, which wouldn't necessarily answer the question.
Plus, volume is not a function of temperature, so that rule would not apply here... I don't believe.

Last edited:

## What is heat capacity?

Heat capacity is the amount of heat energy required to raise the temperature of a substance by one degree Celsius.

## What is an ideal gas?

An ideal gas is a theoretical gas that follows certain assumptions, such as having no intermolecular forces and occupying no volume. This allows for simpler calculations and understanding of gas behavior.

## How is heat capacity of an ideal gas calculated?

The heat capacity of an ideal gas can be calculated using the formula C = (5/2)R, where C is the heat capacity, and R is the gas constant (8.314 J/mol*K).

## Does heat capacity change with temperature for an ideal gas?

No, the heat capacity of an ideal gas remains constant regardless of temperature. This is because the assumptions of an ideal gas do not account for any changes in energy or behavior at different temperatures.

## What factors can affect the heat capacity of an ideal gas?

The heat capacity of an ideal gas can be affected by the number of atoms or molecules in the gas, the specific gas constant, and any external factors such as pressure or volume changes. It can also be affected by any deviations from ideal gas behavior, such as intermolecular forces or non-zero volume.

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