Question

When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 183 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 61 cubic inches

Answer 1

42 pounds per square inches.

Explanation:

The temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas.

⇒
`V\propto (1)/(P)`

or

`V_1P_1=V_2P_2`

Volume, V₁ = 183 cubic inches

Pressure, P₁ = 14 pounds/square inch

We need to find the new pressure if the volume is decreased to 61 cubic inches. Let P₂ is new pressure. So,

`P_2=(V_1P_1)/(V_2)\\\\P_2=(183* 14)/(61)\\\\P_2=42\ \text{pounds per square inch}`

Hence, the final pressure is 42 pounds per square inches.