Question

The volume of a gas inside a flexible container with a temperature of 280 K increasesfrom 3.96 L to 8.28 L.What will be the new temperature of the container?

Answer 1

Step-by-step explanation

Given that;

The initial temperature of the gas 280K

The initial volume of the gas is 3.96L

The final volume of the gas is 8.28L

Follow the steps below to find the final temperature of the gas

In the given data, the pressure is fixed and Charles's law is applicable to the system

Charle's law states that the volume of a given mass is directly proportional to its temperature of the gas provided the pressure remains constant.

Mathematically

`\begin{gathered} \text{ V}\propto\text{ T} \\ \text{ Introduce a proportionality constant} \\ \text{ V = kT} \\ \text{ Isolate k} \\ \text{ k = }\frac{\text{ V}}{\text{ T}} \\ \text{ } \\ \text{ }\frac{\text{ V1}}{\text{ T1}}\text{ }=\text{ }\frac{\text{ V2}}{\text{ T2}} \end{gathered}`

Substitute the given data into the above formula to find the final volume of the gas

`\begin{gathered} \text{ }\frac{3.96}{\text{ 280}}\text{ }=\text{ }\frac{\text{ 8.28}}{\text{ T2}} \\ \text{ cross multiply} \\ \text{ 3.96 }*\text{ T2 }=\text{ 8.28 }*\text{ 280} \\ \text{ 3.96T2 = 2318.4} \\ \text{ Divide both sides by } \\ \text{ }(3.96T2)/(3.96)\text{ = }(2318.4)/(3.96) \\ \text{ T2 = 585.5K} \end{gathered}`

The final temperature of the gas is 585.5K