For each degree rise in temperature , the volume of a gas increases by ……. Of the original volume of the gas at `0^(@)C`.

Options

A. `273.15`
B. `1//273.15`
C. `(273.15)^(2)`
D. `(1//273.15)^(2)`

Answer

B

Explanation

If the pressure is held constant , the ratio of the volume `(V_(2))` of a given mass of air at `100^(@) C` to its volume `(V_(1))` at `0^(@)C` is constant and is independent of the initial volume.
Experiments show that this ratio is `1.366`,i.e.,
`(V_(2))/(V_(1)) = 1.366`
`V_(2) = 1.366 V_(1) = V_(1)(1 + 0.366)`
`= V_(1) + 0.366 V_(1)`
Thus implies that the volume of the gas at `100^(@)C` is greater than its volume at `0^(@)C` by `0.366` times its volume at `0^(@)C`. Since this expansion is for `100^(@)` change in temperature and since this expansion is found to be uniform, it follows that the expansion per unit degree will be by `(0.366//100)V_(1)`or `(1//273)V_(1)`.