Question

About Charles's Law I have a confusion?

Answer 1

The equation for Charles's law is

`ulbar(|stackrel(" ")(" "(T_1)/(V_1) = (T_2)/(V_2)" ")|)" "` (constant pressure and quantity of gas)

The problem says that the volume of the gas increases by `1/273` times its original volume at `0` `""^"o""C"` for every temperature degree it rises.

If we make the final temperature `T_2` be equal to `1 +-` the original temperature, then we have

`T_2 = T_1 +-1`

Or

`(T_1)/(V_1) = (T_1+-1)/(V_2)`

Solving for the final volume, `V_2`, we get

`V_2 = V_1 +-(V_1)/(T_1)`

The temperature `0` `""^"o""C" = 273` `"K"`, so if we make that be the original temperature:

`color(red)(ulbar(|stackrel(" ")(" "V_2 = V_1 +-(1/273)V_1" ")|)`

(the units canceled out when we solved for `V_2`)

Or, in words, the final volume is equal to the original volume plus or minus `1/273` times the original volume.