Question

How hot would a 2.3 L balloon have to get to expand to a volume of 3.0 L, assuming the initial temperature of the balloon is 24°C, and that the pressure inside the balloon remains constant?

Answer 1

The temperature needs to be 390 K.

Explanation:

This is an example of Charles' law, which states that the volume of a gas held at constant pressure varies directly with the Kelvin temperature. The equation for this law is:

`V_1/T_1=V_2/T_2`

Given/Known
`V_1="2.3 L"`
`T_1=24^@"C"+273.15="297 K"`
`V_2="3.0 L"`

Unknown
`T_2`

Solution
Rearrange the equation to isolate `T_2`, substitute the values into the equation and solve.

`V_1/T_1=V_2/T_2`

`T_2=(T_1V_2)/(V_1)`

`T_2=((297"K")xx(3.0"L"))/(2.3"L")`

`T_2="390 K"` rounded to two significant figures.