Fig shows of `PV//T` versus P for `1.00 xx 10^(-3) kg` of oxygen gas at two different temperatures.
(a) What does the dotted plot signify ?
(b) Which is true : `T_(1) lt T_(2) or T_(2) lt T_(1) ?`
( c) What is the value of `PV//T` where the curves meet on the Y-axis ?
(d) If we obtained similar plot for `1.00 xx 10^(-3) kg` of hydrogen, would we get the same value of `PV//T` at the point where the curves meet on the y-axis ? If not, what mass of hydrogen yield the same value of `PV//T` (for low pressure high temperature region of the plot) ? (Molecular mass of `H = 2.02 u`, of `O = 32.0 u, R = 8.31 J "mol"^(-1) K^(-1)`

Explanation

(a) The dotted plot shows that `(PV)/(T) (= mu R)` is a constant quantity, independent of pressure P. This signifies the ideal gas behaviour.
(b) The curve at temperature `T_(1)` is closer to the dotted plot than the curve at temperature `T_(2)`.As the behaviour of a real approaches the behaviour of a perfect gas when temperature is increased, therefore, `T_(1) gt T_(2)`.
(c) Where the two curves meet, the value of `PV//T` on Y-axis is equal to `mu R`.
As mass of oxygen gas = `1.00 xx 10^(-3)Kg = 1g :. (PV)/(T) = mu R = (1/32) xx 8.31 KJ^(-1) = 0.26 JK^(-1)`
(d) If we obtained similar plots for `1.00 xx 10^(-3) kg` of hydrogen , we will not get the same value of `PV//T` at the point , where the curves meet on the Y- axis . This is because molecular mass of hydrogen is different form that of oxygen.
For the same value of `(PV)/T` , mass of hydrogen required is obtained from
`(PV)/(T) = mu R = m/(2.02) xx 8.31 = 0.26`
`m=(2.02 xx 0.26)/(8.31) gram = 6.32 xxx 10^(-2) gram`.