A gas tank has a volume of 25.0 L and a pressure of 16.1 atm. The temperature of...

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September 2022 1 3 Report

A gas tank has a volume of 25.0 L and a pressure of 16.1 atm. The temperature of the gas is 30 degrees Celcius. What is the Celsius temperature when the gas is put in an 8.3 L tank with a pressure of 24 atm? (Combined Gas Law)

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Tokamak

SOLUTION:

Step 1: List the given values.

$\begin{aligned} P_1 & = \text{16.1 atm} \\ V_1 & = \text{25.0 L} \\ T_1 & = 30^{\circ}\text{C} = \text{303 K} \\ P_2 & = \text{24 atm} \\ V_2 & = \text{8.3 L} \end{aligned}$

Step 2: Calculate the final temperature in kelvin by using combined gas law.

$\begin{aligned} T_2 & = \frac{T_1P_2V_2}{P_1V_1} \\ & = \frac{(\text{303 K})(\text{24 atm})(\text{8.3 L})}{(\text{16.1 atm})(\text{25.0 L})} \\ & = \text{150 K} \end{aligned}$

Step 3: Converting the final temperature from kelvin to degree Celsius.

$\begin{aligned} t_2 & = T_2 - 273 \\ & = 150 - 273 \\ & = \boxed{-123^{\circ}\text{C}} \end{aligned}$

Hence, the final temperature is -123°C.

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