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?

1 Answer
Aug 31, 2016

Answer:

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.