Question

To what temperature must a sample of helium gas be cooled from 148°C to reduce its volumefrom 4.8 L to 0.29 L at constant pressure?Answer in units of K.

Answer 1

the final temperature of the gas is 25.4K

Step-by-step explanation

Given that;

The initial temperature of the gas is 148 degrees Celcius

The initial volume of the gas is 4.8L

The final volume of the gas is 0.29L

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

In the given data, the pressure of the gas is fixed. So, apply Charles' law to find the final temperature of the gas

Step 1; State Charles's law

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

Mathematically,

`\begin{gathered} \text{ V }\propto\text{ T} \\ \text{ Introduce proportionality constant} \\ \text{ V = kT} \\ \text{ Divide both sides by T} \\ \text{ }\frac{\text{ V}}{\text{ T}}\text{ = k} \\ \text{ Hence, }\frac{\text{ V1}}{\text{ T1}}\text{ = }\frac{\text{ V2}}{\text{ T2}} \end{gathered}`

Step 2; Convert the temperature to degrees Kelvin

`\begin{gathered} \text{ T K = t}\degree C\text{ + 273.15} \\ \text{ T K = 148 + 273.15} \\ \text{ T K = 421.15K} \end{gathered}`

Step 3; Substitute the given data into the formula in step 1

`\begin{gathered} \text{ }\frac{\text{ V1}}{\text{ T1}}\text{ = }\frac{\text{ V2}}{\text{ T2}} \\ \\ \text{ }\frac{\text{ 4.8}}{\text{ 421.15}}\text{ = }\frac{\text{ 0.29}}{\text{ T2}} \\ \text{ Cross multiply} \\ \text{ 4.8 }*\text{ T2 = 421.15 }*\text{ 0.29} \\ \text{ 4.8 T2 = 122.1335} \\ \text{ Divide both sides by 4.8} \\ \text{ }\frac{\cancel{4.8}T2}{\cancel{4.8}}\text{ = }(122.1335)/(4.8) \\ \text{ T2 = 25.4K} \end{gathered}`

Therefore, the final temperature of the gas is 25.4K