The three diagrams below depict three different processes for a given mass of an ideal gas. What information can be drawn regarding the change of (a) pressure, (b) volume and (c ) temperature of the gas from the plots as shown in Fig., respectively.

Explanation

(a) As the given curve is a straight line with positive slope and negative intercept the V-axis, its equation will be
`V = aT - b` `(as = mx - c)`
So the gas equation `PV = mu RT` in the light of above yields
`P = (mu RT)/(V) = (mu RT)/(aT - b) = (mu R)/(a - (b//T)`
Now from Fig. `T_(2) gt T_(1)`, so `P_(2) lt P_(1)`.
(b) As the given curve is straight line with positive slope and positive intercept with the P-axis, its equation will be
`P = aT + b` `(as y = mx + c)`
So the gas equation `PV = mu RT` in the light of above yeilds
`V = (mu RT)/( P) = (mu RT)/(aT + b) = (mu R)/(a + (b//T)`
Now from Fig. `T_(2) gt T_(1)` so `V_(2) gt V_(1)`.
(c ) As the given curve is a straight line with negative slope and positive intercept with the P-axis, its equation will be
`P = -V + b` `("as" y = mx + c)`
So the gas equation `PV = mu RT` in the light of above yields
`(- aV + b) V = mu RT`.
This is the equation of a parabola as shown in Fig. So during expansion, the temperature of gas first increases, reach a maximum and then decreases.