A gas is filled in a vessel of volume V at 35 degree centigrade.To what temperature should it be heated in order that half of the gas may escape out?

Question

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Answer 1 · 2018-01-14T20:23:18

The new temperature should be 343 °C.

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

In your problem, we must calculate the temperature at which the new volume will be twice the original volume. We have

#V_1 = V; color(white)(l)T_1 = "35 + 273.15 K = 308.15 K"#
#V_2 = 2V; T_2 = "?"#

∴ #T_2 = "308.15 K" × (2 cancel(V))/(cancelV) = "616.30 K = 343 °C"#

The new temperature is 343 °C.