An insulated container containing monoatomic gas of molar mass s is moving with a velocity `v_0`. If the container is suddenly stopped, find the change in temperature.

Options

A. `mv_(0)^(2)/(2R)`
B. `mv_(0)^(2)/(3R)`
C. `3mv_(0)^(2)/2 R`
D. `5mv_(0)^(2)/3 R`

Answer

B

Explanation

When the container stops, its total kinetic energy is transferred to gas molecules in the form of translational kinetic energy. Thereby increasing the absolute temperature.
Assuming n = number of moles
Given m = molar mass of the gas
If `Delta T` = change in absolute temperature
Then, kinetic energy of molecules due to velocity `v_(0)`,
`Delta K_(motio n) = 1/2 (mn)v_(0)^(2)` ..(i)
Increase ub translational kinetic energy
`Delta K_(translatio n) = n 3/2 R(Delta T)` ..(ii)
According to kinetic theory eqs. (i) and (ii) are equal
`implies 1/2(mn)v_(0)^(2) = n 3/2 R(DeltaT)`
`(mn)v_(0)^(2) = n3R(Delta T)`
`implies Delta T = ((mn)v_(0)^(2))/(3nR) = (mv_(0)^(2))/(3R)`.