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 93 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 31 cubic inches.

Answer 1

The new pressure of the gas is 42 pounds per square inches.

Explanation:

When the temperature remains constant, the volume of a gas is inversely proportional to the pressure of the gas.

`V\propto (1)/(P)`

We can rewrite the above equation is

`(V_1)/(V_2)=(P_2)/(P_1)` [at constant temperature]

At a pressure of 14 pounds per square inches, a balloon is filled with 93 cubic inches of gas.

The volume of the gas is decreased to 31 cubic inches.

Here,

`V_1`= 93 cubic inches,
`P_1` = 14 pounds per square inches,

`V_2`=31 cubic inches,
`P_2` = ?

`(V_1)/(V_2)=(P_2)/(P_1)`

`\Rightarrow (93)/(31)=(P_2)/(14)`

`\Rightarrow (P_2)/(14)=(93)/(31)`

`\Rightarrow {P_2}=(93)/(31)* 14`

`\Rightarrow {P_2}=42` pounds per square inches

The new pressure of the gas is 42 pounds per square inches.