Answer to Question #316777 in Molecular Physics | Thermodynamics for Fritz malazarte

Question

The temperature of an ideal gas remains constant while the absolute pressure changes from 100 kpa to 800 kpa. If initial volume is 100 liters, what is the final volume in liters?

Answer 1

Ideal gas law

P₁V₁ = nRT₁ ________eqⁿ(1)

P₂V₂ = nRT₂ _________eqⁿ(2)

From the given conditions,

Pressures and Volumes are vary, but the Temperatures, number of moles remains constant.

And R is the universal gas constant

So,the above equations becomes

$P_{1}V_{1}=P_{2}V_{2}\>\>equation (3)$

$P_{1}=100\>kpa\\P_{2}=800\>kpa\\V_{1}=100\>liters\\V_{2}=final\>Volume=?$

Put all the above values in equation (3)

$P_{1}V_{1}=P_{2}V_{2}$

${100kpa}\times{100liters}={800kpa}\times{V_{2}}$

$V_{2} = [\frac{100kpa}{800kpa}][100liters]\\V_{2} = 12.5\>liters$

$V_{2}=12.5\>liters$

So, the final Volume V₂ is 12.5 liters