We have two equal size boxes, A and B . Each box contains gas that behaves as an ideal gas. The pressure of the gas in box A is 0.20 atm and the pressure of the gas in box B is 0.04 atm. This is all we know about the gas in the boxes. Which of the following statements MUST be true ?

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The temperature in A is higher than in B

The total translational kinetic energy of all molecules is greater in gas A than in gas B

There are more molecules in A than in B

The molecules in A are moving faster than those in B

answer is D.

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Detailed Solution

$\begin{array}{l} P V = \frac{1}{3} m N {(v_{r m s})}^{2} (h e r e V = c o n s \tan t) \\ \Rightarrow P V = \frac{1}{3} m N v_{r m s}^{2} = \frac{2}{3} {(K . E_{\max})}_{t r a n s l a t i o n a l} \\ \Rightarrow {(K . E_{\max})}_{t r a n s l a t i o n a l} \propto P \\ P r e s s u r e o f A i s h i g h e r, s o t h e t o t a l t r a n s l a t i o n a l k i n e t i c e n e r g y o f \\ a l l m o l e c u l e s i s g r e a t e r i n g a s A t h a n i n g a s B . \\ A l l t h e o t h e r s t a t e m e n t s m a y b e t r u e b u t n o t m u s t b e t r u e . \end{array}$