Question

An expandable ball holds 5 L of air at 1 atm pressure and at a temperature of 293K. If it is submerged in the ocean to a depth where the pressure is 1.75 atm and the temperature is 275K, what would the new volume be?

Answer 1

Expandable Ball contains same number of moles in both the situations.

According to ideal gas law,

$PV = nRT$

P = pressure at that temperature and volume

V = volume at ₁that pressure and temperature

T = temperature at that pressure and volume

R = universal gas constant

n = number of moles

In this case as expandable ball is closed structure,so,no of moles is constant.

So,

$n=constant; R= constant$

So,

PV=nRT

$nR=PV/T$ $=constant$ ------(a)

Now,according to question there are two situations.

Situation 1 :

P₁$=1atm$

V₁$=5L$

T₁$=293K$

Situation 2 :

$P2=1.75atm$

T₂ $=275 K$

We have to find new volume V₂ :

Using equation (a);

P₁V₁/T₁$=$ P₂V₂/T₂

V₂$=P$₁V₁T₂/T₁P₂

V₂ $=(1×5×275)/(1.75×293)$

V₂ $= 2.682 L$ (Answer)