Question

A gas with an initial volume of 5*10-3 m3 and an initial pressure of 300 kPa is expanded to a final volume of 10*10-3 m3 and a final pressure of 50 kPa. If the initial temperature of the gas was 200 K, what is the final temperature?

Answer 1

Given:

• Initial volume, V1 = 5 x 10⁻³ m³

,

• Initial pressure, P1 = 300 kPa

,

• Final volume, V2 = 10 x 10⁻³ m³

,

• Final pressure, P2 = 50 kPa.

,

• Initial temperature, T1 = 200 K

Let's find the final temperature.

To find the final temperature, apply the combined gas law:

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

Now, rewrite the formula for final temperature, T2:

`T_2=(P_2V_2T_1)/(P_1V_1)`

Input values into the equation for T2 and evaluate:

`T_2=(50*(10*10^(-3))*200)/(300*(5*10^(-3)))`

Solving further:

`\begin{gathered} T_2=(100)/(1.5) \\ \\ T_2=66.67\text{ K} \end{gathered}`

Therefore, the final temperature is 66.67 K.

ANSWER:

66.67 K