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

Explanation

According to kinetic interpretation of temperature, absolute temperature of a given sample of a gas is proportional to the total translational kinetic energy of its molecules. Hence, any change in absolute temperature of a gas will contribute to corresponding change in translational KE and vice- versa.
`"Given"" "m = "Molar mass of the gas"`
When , the container stops , its total KE is transferred to gas molecules in the form of translational KE, thereby increasing the aboslute temperature .
If `DeltaT =` change in absolute temperature.
Then ,KE of molecules due to velocity `V_(0), KE = 1/2 (mn) V_(0)^(2)" " ........(i)`
increase in translational `KE =n3/2R(DeltaT)" ".......(ii)`
According to kinetic theory Eqs. (i) and (ii) are equal
`rArr " "1/2 (mn)v_(0)^(2) =n 3/2 R (DeltaT)`
`(mn) v_(0)^(2) =n3R (DeltaT)`
`rArr " " DeltaT =((mn)v_(0)^(2))/(3nR)`
`rArr " " DeltaT =(mv_(0)^(2))/(3R)`