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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.
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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