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Question

A sample of a gas contains N1 molecules and the total kinetic energy at 123C is E1 ergs. Another sample of a gas at 27C has a total kinetic energy as 2E1 ergs. Assuming gases to be ideal, the number of gas molecules in the second sample will be:

A
N1
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B
N1/2
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C
2N1
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D
4N1
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Solution

The correct option is A N1
The total kinetic energy of a gas is proportional to the temperature of the gas molecules and the number of molecules present in the sample.

KE = 32×N×K×T

where, K is the Boltzman's constant, T is the temperature and N is the number of molecules of gas.

In the first case, KE1 = 32×K×150×N1

In the second case, KE2 = 32×K×300×N2

KE2KE1=2

2N2N1=2

2N2=2N1

N2=N1

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