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Question
A vessel containing one mole of a monatomic ideal gas (molecular weight = 20 g mol−1) is moving on a floor at a speed of 50 m s−1. The vessel is stopped suddenly. Assuming that the mechanical energy lost has gone into the internal energy of the gas, find the rise in its temperature.
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Solution
Number of moles of the ideal gas, n = 1 mole
Molecular weight of the gas, W = 20 g/mole
Mass of the gas, m =20 g
Velocity of the vessel, V = 50 m/s
Decrease in K.E. of the vessel = Internal energy gained by the gas
`"K""E" = 1/2 "m"("u"^2 -"v"^2)`
`"K""E" = 1/2 xx 20 xx 10^-3 xx (0-50 xx 50)`
KE = -25 J = gain in internal energy of the gas change in internal energy of a gas `d/2n R(triangle"T")`
where d is the degree of freedom of the gas F or a monoatomic gas , d=3.
So, 25 = ` 3/2 n R (triangle T)`
`=> 25 = 1 xx 3/2 xx 8.31 xx triangle T`
`=> triangle T = 50 /(3 xx 8.3) = 2 "K"`
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