Question

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 0.1m ^ 3 of volume, what is the new pressure of the gas? О O O 1 atm 10 atm 0.10 atm

Answer 1

10 atm

Step-by-step explanation:

Assuming the gas is kept at constant temperature, we can apply the following law (Boyle's law):

"For a gas kept at a constant temperature, the pressure of the gas is inversely proportional to its volume"

Mathematically,

`pV=const.`

where p is the pressure of the gas and V its volume.

The equation can also be rewritten as

`p_1 V_1 = p_2 V_2`

Where for the gas in the problem, we have:

`p_1 = 2 atm` is the initial pressure

`V_1 = 0.5 m^3` is the initial volume

`p_2` is the final pressure

`V_2 = 0.1 m^3` is the final volume

Solving for p2,

`p_2 = (p_1 V_1)/(V_2)=((2)(0.5))/(0.1)=10 atm`