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 TA and TB respectively is..

a) TA = TB

b) TA = 2TB

C) TA = 1/2 TB

d) TA = 1/?2 TB

e) TA = 1/4 TB

Answer 1

The correct statement regarding the absolute temperatures of Container A and Container B, given that Container A has twice as many molecules and pressure is the same, is TA = 1/2 TB.

Step-by-step explanation:

To determine the relationship between the absolute temperatures TA and TB in containers A and B, we can apply the Ideal Gas Law, which is PV = nRT. In this scenario, the volume (V) and pressure (P) are held constant in both containers, while container A has twice the number of molecules (n), which implies twice the number of moles of gas. Because R, the gas constant, is always the same, the relationship boils down to comparing nT for both containers.

Since the pressure is the same and the volume is also the same, for the pressure to remain constant with twice the number of moles in container A, the temperature must be halved, which means TA = 1/2 TB. Therefore, the correct statement regarding the absolute temperatures TA and TB is:

c) TA = 1/2 TB

Answer 2

option (c)

Step-by-step explanation:

nA = 2 nB

VA = VB

PA = PB

By use of ideal gas equation

PV = n RT

Where, P is pressure, V is volume, R is the gas constant.

Here, P, V, R are constant.

nT = Constant

`(T_(A))/(T_(B))=(n_(B))/(n_(A))`

`(T_(A))/(T_(B))=(n_(B))/(2n_(B))`

`T_(A)=(T_(B))/(2)`