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An insulated container monoatomic gas of...

An insulated container monoatomic gas of molar mass m is moving with a velocity `nu_(0)`. If the container is suddenly stopped. Find the change in temperature.

Text Solution

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Suppose the container has n moles of the monoatomic gas. Then the loss in K.E. of the gas
`DeltaE=1/2(mn)nu_(O)^(2)`
If the temperature of the gas change by `DeltaT,` then heat gained by the gas,
`DeltaQ=nC_(V)DeltaT`
`DeltaQ=3/2 nRDeltaT`
Now, DeltaQ=DeltaE
`3/2nDeltaT=1/2(mn)nu_(O)^(2)`
`DeltaT=(mnu_(O)^(2))/(3R)`
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