# Derive the density of an ideal gas as a function of temperature?

• Outrageous
In summary, the density of an ideal gas as a function of temperature is related to the molecular weight of the gas and the volume of the gas.
Outrageous
derive the density of an ideal gas as a function of temperature??

## Homework Statement

Derive the density of an ideal gas when it is allowed to expand as a function of temperature when pressure is kept constant/

## The Attempt at a Solution

density= PM/(RT) , where M is the molecular weight
or ∂ρ/∂T =M/(RT)
or ρ(V,P),then keep P constant, ∂ρ/∂V =∂<PM/(RT)>

actually i am not sure what the question asking about . Thank you

Outrageous said:

## Homework Statement

Derive the density of an ideal gas when it is allowed to expand as a function of temperature when pressure is kept constant/

## The Attempt at a Solution

density= PM/(RT) , where M is the molecular weight
or ∂ρ/∂T =M/(RT)
or ρ(V,P),then keep P constant, ∂ρ/∂V =∂<PM/(RT)>

actually i am not sure what the question asking about . Thank you
Relate the mass of the gas to the volume using the ideal gas equation. Use n = m/M where m is the mass of the gas and M is the molecular weight or mass/mole of the gas.

What is n/V? How is n/V related to density of the gas?

AM

m/V is density of gas system
n /V is density of gas molecule?
I don't know how to relate.

Outrageous said:
m/V is density of gas system
... and since m = nM... the density of the gas is ... (in terms of M, P, R and T).

AM

Outrageous said:

## Homework Statement

Derive the density of an ideal gas when it is allowed to expand as a function of temperature when pressure is kept constant/

## The Attempt at a Solution

density= PM/(RT) , where M is the molecular weight
or ∂ρ/∂T =M/(RT)
or ρ(V,P),then keep P constant, ∂ρ/∂V =∂<PM/(RT)>

actually i am not sure what the question asking about . Thank you

So the question want density in terms of P M R T? Then why does the question say when it expand?

Outrageous said:
So the question want density in terms of P M R T? Then why does the question say when it expand?
You should ask the person who drafted the question...it was probably asked this way to just give it some context. What the question is asking is the relationship between T and m/V with constant P. Whether it is expanding or being compressed at constant P makes no difference to the relationship.

AM

Andrew Mason said:
Whether it is expanding or being compressed at constant P makes no difference to the relationship.

AM

Thank you.

## 1. What is an ideal gas?

An ideal gas is a theoretical gas composed of molecules that do not have any volume or intermolecular forces. This means that the molecules in an ideal gas do not take up space and do not interact with each other.

## 2. What is the relationship between temperature and density in an ideal gas?

According to the ideal gas law, the density of an ideal gas is directly proportional to its temperature. This means that as the temperature of an ideal gas increases, its density also increases.

## 3. How is the density of an ideal gas calculated?

The density of an ideal gas can be calculated using the ideal gas law, which states that the density (ρ) is equal to the product of the gas constant (R), temperature (T), and pressure (P), divided by the molar mass (M) of the gas: ρ = (PM)/(RT).

## 4. How does the density of an ideal gas change at different temperatures?

As mentioned before, the density of an ideal gas is directly proportional to its temperature. This means that as the temperature increases, the density also increases. On the other hand, as the temperature decreases, the density also decreases.

## 5. Can the density of an ideal gas be changed?

The density of an ideal gas can be changed by changing its temperature or pressure. However, this only applies to ideal gases, as real gases will have intermolecular forces and non-zero volumes that can affect their density.

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