Question

The temperature of a sample of gas in a steel tank at 35.0 kPa isincreased from -150.0°C to 28.0 °C. What is the final pressure insidethe tank?

Answer 1

The final pressure inside the tank is 86.0kPa

Step-by-step explanation

Given that:

The initial pressure of the gas is 35.0kPa

The initial temperature of the gas is -150 degrees Celcius

The final temperature of the gas is 28 degrees Celcius

Follow the steps below to find the final pressure inside the tank

The volume of the tank is fixed and hence, the process is called Isochoric process

Step 1: Write the gas law for constant volume

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

Step 2: Convert the temperature to degrees kelvin

`\begin{gathered} t1\text{ }=-150\degree C \\ T=\text{ t }+\text{ 273.15} \\ \text{ T }=\text{ -150 }+\text{ 273.15} \\ \text{ T }=\text{ 123.15K} \\ \\ t2\text{ }=\text{ 28}\degree C \\ T\text{ }=\text{ t }+\text{ 273.15} \\ \text{ T }=\text{ 28}+273.15 \\ T\text{ }=\text{ 301.15K} \end{gathered}`

Step 3: Substitute the given data into the formula in step 1 to find P2

`\begin{gathered} (35)/(123.15)=(P2)/(301.15) \\ \text{ Cross multiply} \\ P2*\text{ 123.15}=\text{ 35}*\text{ 301.15} \\ P2*123.15\text{ }=\text{ 10540.25} \\ \text{ Divide both sides by 123.15} \\ \text{ P2 }=\text{ }(10540.25)/(123.15) \\ \text{ P2 }=85.58kPa \\ P2\approx86.0kPa \end{gathered}`

Hence, the final pressure inside the tank is 86.0kPa