Question

A balloon with a volume of 5.3 L is taken from an indoor temperature of 24 C to the outdoors. The volume of the balloon outside is 4.9 L. How do you determine the C temperature outside?

Answer 1

The outside temperature is 0 °C.

Explanation:

Given

The volume `V_1` of a gas at a temperature `T_1`.
A second volume `V_2`

Find

The second temperature `T_2`

Strategy

A problem involving two gas volumes and two temperatures must be a Charles' Law problem.

The formula for Charles' Law is

`color(blue)(|bar(ul(color(white)(a/a) V_1/T_1 = V_2/T_2color(white)(a/a)|)))" "`

Solution

We can rearrange Charles' Law to get

`T_2 = T_1 × V_2/V_1`

In your problem,

`V_1 = "5.3 L"`; `T_1 = (24 + 273.15) K = "297.15 K"`
`V_2 = "4.9 L"`; `T_2 = "?"`

∴ `T_2 = "297.15 K" × (4.9 cancel("L"))/(5.3 cancel("L")) = "274 K"`

`"200 K" = "(274 - 273.15) °C" = "0 °C"`

The outside temperature is 0 °C.