Two containers of equal volume each hold samples of the same ideal gas. Container A has twice as many molecules as container B . If the gas pressure is the same in the two containers, the correct statement regarding the absolute temperatures $T _ { A } \text { and } T _ { B }$ in containers A and B, respectively, is
A) $T _ { A } = T_ {B}$
B) $T _ { A } = \frac { 1 } { 2 } T _ { B }$
C) $T _ { \mathbf { A } } = \frac { 1 } { \sqrt { 2 } } T _ { \mathrm { B } }$
D) $T _ { \mathbf { A } } = 2 T _ { \mathbf { B } }$
E) $T _ { A } = \frac { 1 } { 4 } T _ { B }$

Question

Two containers of equal volume each hold samples of the same ideal gas. Container A has twice as many molecules as container  B . If the gas pressure is the same in the two containers, the correct statement regarding the absolute temperatures $T _ { A } \text { and } T _ { B }$ in containers A and B, respectively, is
A) $T _ { A } = T_ {B}$
B) $T _ { A } = \frac { 1 } { 2 } T _ { B }$
C) $T _ { \mathbf { A } } = \frac { 1 } { \sqrt { 2 } } T _ { \mathrm { B } }$
D) $T _ { \mathbf { A } } = 2 T _ { \mathbf { B } }$
E) $T _ { A } = \frac { 1 } { 4 } T _ { B }$

Quizplus · Accepted Answer

Since the volume and pressure are the same for both containers but container A has twice as many molecules as container B, according to the ideal gas law (PV = nRT), the temperature in container A must be half that of container B to maintain the same pressure, because the amount of substance (n) is doubled in A. This is because temperature is directly proportional to the product of the number of moles (n) and the gas constant (R) when pressure (P) and volume (V) are constant.

Two Containers of Equal Volume Each Hold Samples of the Same