Question

A sample of an ideal gas initially occupies a volume of 6 L. The pressure of the sample is then doubled while it is cooled to one third its original absolute temperature. After these changes, what volume does the sample occupy?

Answer 1

Answer:

V₂= 1 L

Explanation:

Given that

Volume occupies V₁= 6 L

Initial pressure = P₁

Initial temperature = T₁

The final pressure =P₂ = 2 P₁

Final volume =V₂

Final temperature = T₁/3

As we know that equation for ideal gas

P V = m R T

P=pressure,  V=volume,   T=temperature

m=mass  ,R=gas constant

Now from mass conservation

$m=\dfrac{P_1V_1}{RT_1}=\dfrac{P_2V_2}{RT_2}$

$\dfrac{P_1V_1}{RT_1}=\dfrac{P_2V_2}{RT_2}$

$\dfrac{P_1\times 6}{RT_1}=3\times \dfrac{2P_1V_2}{RT_1}$

6 = 3 x 2 V₂

V₂= 1 L

So the final volume will be 1 L