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Q.

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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a

There are more molecules in  A than in B

b

The molecules in  A are moving faster than those in B

c

The temperature in A  is higher than in  B

d

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

answer is D.

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Detailed Solution

PV=13mNvrms2         here V=constant​⇒PV=13mNvrms2=23K.Emaxtranslational​⇒K.Emaxtranslational∝PPressure of A is higher, so the total translational kinetic energy of all molecules ​is greater in gas  A than in gas  B.All the other statements may be true but not must be true.
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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 ?