Question

An inflated balloon has a volume of 5.75 L at a temperature of 22°C. At what temperature in degrees Celsius will the volume of the balloon decrease to 5.38 L?

Answer 1

The volume will be at `"5.38 L"` when the temperature is at `color(blue)("2.85"^@"C"")`.

Explanation:

This is an example of Charles' law which states that at constant pressure, the volume is directly proportional to the temperature in Kelvins. The equation to use is `V_1/T_1=V_2/T_2`.

Given/Known
`V_1="5.75 L"`
`T_1="22"^@"C""+273.15=295 K"`
`V_2="5.38 L"`

Unknown
`T_2`

Solution
Rearrange the equation to isolate `T_2`. Substitute the known values into the equation and solve. Convert the temperature from Kelvins to degrees Celsius.

`V_1/T_1=V_2/T_2`

`T_2=(T_1V_2)/V_1`

`T_2=((295"K")*(5.38cancel"L"))/(5.75cancel"L")`

`T_2="276 K"`

Convert Kelvins to `""^@"C""`.

`""^@"C""="K-273.15`

`""^@"C"=276-273.15="2.85"^@"C"`