Question

3. A gaspressure of a gas inside the fixed volume container. A thermometerreads a pressure of 258 kPa at 3°C. What is the temperature when ththermometer reads a pressure of 355 kPa?

Answer 1

The final temperature of the gas is 380K

Step-by-step explanation

Given that;

The initial pressure of the gas is 258kPa

The initial temperature of the gas is 3 degrees Celcius

The final pressure of the gas is 355kPa

To find the final pressure of the gas, follow the steps below

In the given data, the volume of the container is fixed. Hence, the process is called isochoric.

Step 1: Write the gas law at constant volume

`\text{ }(P1)/(T1)=(P2)/(T2)`

Step 2: Convert the temperature to kelvin

`\begin{gathered} t1\text{ }=\text{ 3}\degree C \\ T\text{ }=\text{ t }+\text{ 273.15} \\ \text{ T }=\text{ 3}+273.15 \\ \text{ T }=276.15K \end{gathered}`

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

`\begin{gathered} (258)/(276.15)=(355)/(T2) \\ \text{ cross multiply} \\ \text{ 258}* T2\text{ }=\text{ 355}*\text{ 276.15} \\ \text{ 258}* T2=\text{ 98033.25} \\ \text{ Divide both sides by 258} \\ \text{ T2 }=\text{ }(98033.25)/(258) \\ \text{ T2 }=\text{ 379.97K} \\ T2\approx380K \end{gathered}`

Hence, the final temperature of the gas is 380K