Question

A sample of gas in a balloon has an initial temperature of 18 ∘C and a volume of 33 L. If the temperature changes to 47 ∘C, and there is no change of pressure or amount of gas, what is the new volume, V2, of the gas?

Answer 1

The final volume of the sample of gas is 36.287 liters.

Step-by-step explanation:

Let suppose that sample of gas is a closed system, that is, a system with no mass interactions with surroundings, and gas is represented by the equation of state for ideal gases, which is described below:

`P\cdot V = n\cdot R_(u)\cdot T` (1)

Where:

`P` - Pressure, in atmospheres.

`V` - Volume, in liters.

`n` - Molar quantity, in moles.

`T` - Temperature, in Kelvin.

`R_(u)` - Ideal gas constant, in atmosphere-liters per mole-Kelvin.

As we know that sample of gas experiments an isobaric process, we can determine the final volume by the following relationship:

`(T_(1))/(V_(1)) = (T_(2))/(V_(2))` (2)

Where:

`V_(1)` - Initial volume, in liters.

`V_(2)` - Final volume, in liters.

`T_(1)` - Initial temperature, in Kelvin.

`T_(2)` - Final temperature, in Kelvin.

If we know that
`V_(1) = 33\,L`,
`T_(1) = 291.15\,K` and
`T_(2) = 320.15\,K`, then the final volume of the gas is:

`V_(2) = V_(1)\cdot \left((T_(2))/(T_(1)) \right)`

`V_(2) = 33\,L * (320.15\,K)/(291.15\,K)`

`V_(2) = 36.287\,L`

The final volume of the sample of gas is 36.287 liters.