When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P-V curve, V-T curve,P-T curve etc.
For example, P-V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V-T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.
Now, answer the following questions :
Which of the following statements is correct regarding a fixed amount of ideal gas undergoing the following process :

Options

A. Root mean square (RMS) speed of gas molecules increase during the process `AtoB`
B. Density of the gas increases during the process `AtoB`
C. Such a graph is not possible
D. If `P_B=4P_A` then `V_A=4V_B` (where `P_A,V_A, P_B` & `V_B` represent pressure and volume values at states A and B).

Answer

B

Explanation

(A)Temperature decreases during process A to B, so RMS speed decreases (`because V_(RMS)prop sqrtT`)
(B)`d_(gas)=(PM)/(RT)`upon moving from A to B, P increases and temperature decreases.So, density of gas increases.
( C)This graph is possible if during the process :`P prop 1/(V^(1//2))`
`because PT="Constant" therefore P((PV)/(nR))="Constant" :. P^2V="Constant" or PV^(1//2)=` Constant
(D)If `P_B=4P_A`, then `V_A=16V_B`(according to `P^2V` =Constant for process)