Suppose you have a gas under 2 atm of pressure and taking up 0.5m^3 of volume. if you compress the gas so that it takes up .1m^3 of volume, what is the new pressure of the gas?
a) 1atm
b) 10atm
c) 0.10atm

A) 1atm

Explanation:

Let us assume the expansion of gas is isothermal, i.e. there's no change in temperature during expansion. Ususaly this can be bought about by slowly expanding the gas so that the heat transfer is always at the same temperature as the surroundings.

Also, let us assume that the gas is ideal, i.e. it follows the ideal gas equation:

PV = nRT, where,

P -> Preassure

V -> Volume

R -> Universal gas constant

T -> Temperature.

Let P₁,  V₁ and P₂, V₂ be the preassure and volume of the gas before and after the expansion respectively.

Then,

P₁V₁ = nRT₁ , and

P₂V₂ = nRT₂.

But since temperature is constant, T₁ = T₂ = T.

Hence, P₁V₁ = P₂V₂ = nRT

Putting respective values of P₁, V₁ ans V₂, we get:

2atm * 0.5m³ =  P₂ * 1m³

=> P₂ = 1atm

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