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Two perifect gases at absolute temperatu...

Two perifect gases at absolute temperatures `T_(1) and T_(2)` are mixed. The absolute temperature of the mixture is T. there is no loss of energy.If `m_(1) and m_(2)` are masses of molecules and `n_(1) and n_(2)` are number of molecules, then

A

`T=(T_(1)+T_(2))/(2)`

B

`T=(n_(1)T_(1)+n_(2)T_(2))/(n_(1)+n_(2))`

C

`T=(n_(1)T_(1)+n_(2)T_(2))/(T_(1)+T_(2))`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
Average KE per molecule of a gas `=(3)/(2)KT`
Before mixing two gases, the averge KE of all molecules of 2 gases
`=(3)/(2)kn_(1)T_(1)+(3)/(2)kn_(2)T_(2)`
after mixing the average KE of both gases
`=(3)/(2)k(n_(1)+n_(2))T`
where,T is temperature of mixture
`therefore` No loss of enegy.
`therefore` " " `(3)/(2)k(n_(1)+n_(2))T=(3)/(2)kn_(1)T_(1)+(3)/(2)kn_(2)T_(2)`
`T=(n_(1)T_(1)+n_(2)T_(2))/(n_(1)+n_(2))`
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