Question

question 3 (5 points)
listen
which graph shows the pressure - temperature relationship for a gas at a fixed volume?
a) graph a
b) graph b
c) graph c
d) graph d

Explanation:

To determine the correct graph for the pressure - temperature relationship of a gas at fixed volume, we use Gay - Lussac's Law. This law states that for a gas with constant volume, the pressure (\(P\)) is directly proportional to the absolute temperature (\(T\)), i.e., \(P\propto T\) (or \(P = kT\) where \(k\) is a constant). A direct proportionality between two variables is represented by a straight - line graph passing through the origin (since when \(T = 0\) (in absolute temperature scale), \(P=0\)).

• Graph A: It is a straight line passing through the origin, which is consistent with the direct proportionality between pressure and temperature for a gas at fixed volume.
• Graph B: It shows pressure as constant with respect to temperature, which does not follow Gay - Lussac's Law.
• Graph C: It shows temperature as constant with respect to pressure, which is not in line with the law.
• Graph D: It shows an inverse relationship (a hyperbolic curve) between pressure and temperature, which would be the case for Boyle's Law (where volume is not constant and \(P\propto\frac{1}{V}\) at constant \(T\)), not Gay - Lussac's Law.

Answer:

A) Graph A