Question

A certain amount of oxygen gas in a container of volume 1.5 x 10^-2 m^3 has a temperature of 302 K and at a pressure of 2.5 x 10^5 Pa. After some of the oxygen gas is allowed to escape from the container, the pressure drops to 1.2 x 10^5 Pa. How much (in SI unit) the gas has escaped?​

Answer 1

Ve = 0.01625 [m³]

Step-by-step explanation:

This type of problem can be solved by the following expression.

`P_(i)*V_(i)*T_(o)=P_(o)*V_(o)*T_(i)`

where_

Pi = Initial pressure = 2.5 x 10⁵ [Pa]

Vi = initial volume = 1.5 x 10⁻² [m³]

To = final temperature = 302 [K]

Po = final pressure = 1.2 x 10⁵ [Pa]

Vo = final volume [m³]

Ti = initial temperature = 302 [K]

Now the key to solving this problem is to make it clear that the temperature remains constant throughout the process. That is, it does not change.

`2.5*10^(5)*1.5*10^(-2) *302 = 1.2*10^(5)*V_(o)*302\\1132500=36240000*V_(o)\\V_(o)=0.03125 [m^(3) ]`

But this calculated volume corresponds to the volume of the tank, now by means of the difference between the initial volume and the final volume we can calculate the volume of gas that escaped.

`V_(e)=0.03125-0.015\\V_(e)=0.01625 [m^(3) ]`