Question

Container A and container B hold samples of the same ideal gas. The volume and the pressure of container A is equal to the volume and pressure of container B, respectively. If Container A has half as many molecules of the ideal gas in it as Container B does, then which of the following mathematical statements is correct regarding the absolute temperatures TA and TB in Container A and Container B. respectively?

A. TA = TB/2.
B. TA = 4TB.
C. TA = TB/4.
D. TA = 2TB.
E. TA = TB

Answer 1

A. TA = TB/2.

Step-by-step explanation:

Since container A has half as many molecules of the ideal gas in it as container B. Therefore, container A will have half the volume of gas as in container B:

`V_A = (1)/(2)V_B`

Now, from Charle's Law:

`(V_A)/(T_A)=(V_B)/(T_B)\\\\(1)/(2)(V_B)/(T_A)=(V_B)/(T_B)\\\\T_A = (T_B)/(2)`

Hence, the correct option is:

A. TA = TB/2.