Question

The volume of gas in a balloon is 1.90L at 41C. The balloon is heated, causing it to expand to a volume of 5.70L. What is the new temperature of the gas inside the balloon?

Answer 1

The new temperature of the gas is 669 °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)|)))" "`

Rearrange Charles' Law to get

`T_2 = T_1 × V_2/V_1`

Solution

`V_1 = "1.90 L"; T_1 = "41 + 273.15 K = 314.15 K"`
`V_2 = "5.70 L"; T_2 = "?"`

∴ `T_2 = "314.15 K" × (5.70 cancel("L"))/(1.90cancel"L") = "942.45 K = 669 °C"`

The new temperature is 669 °C.