Pressure versus temperature graph of an ideal gas of equal number of an ideal gas of equal number of mole of defferent volumes are platted as shown in figure. 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.