Pressure versus temperature graph of an ideal gas of equal number of moles of different volumes is plotted as shown in Fig. Choose the correct alternative.

Options

A. `V_(1) = V_(2), V_(3) = V_(4)` and `V_(2) gt V_(3)`
B. `V_(1) = V_(2), V_(3) = V_(4)` and `V_(2) lt V_(3)`
C. `V_(1) = V_(2), V_(3) = V_(4)`
D. `V_(4) = V_(3) gt V_(2) gt V_(1)`

Answer

A

Explanation

a. From ideal gas equation,
`PV = mu RT`
`:. P = (mu RT)/(V) T`
Comparing, this equation with `y = mx`
slope of line, `tan theta = m mu R//V`
i.e., `V prop (1)/(tan theta)`
It means line of smaller slope represents greater volume of gas
For the given problem figue
Point 1 and 2 are on the same line, so they will represent same volume, i.e., `V_(1) = V_(2)`
Similarly point 3 and 4 are on the same line, so they will represent same volume `V_(3) = V_(4)`, ltbRgt But `V_(1) gt V_(3) (= V_(4)` or `V_(2) gt V_(3) = V_(4)` as slope of line `-2` is less than that of 3-4.