The temperature of a mono-atomic gas in an uniform container of length `L` varies linearly from `T_(0)"to"T_(L)` as shown in the figure. If the molecular weight of the gas is M, then the time taken by a wave pulse in traveling from end A to end B is

Options

A. `(2L)/(sqrt(T_(L))+sqrt(T_(0)))sqrt((3M)/(5R))`
B. `sqrt((3(T_(L)-T_(0)))/(5RML)`
C. `(2L)/(sqrt(T_(L))-sqrt(T_(0)))sqrt((3M)/(5R))`
D. `Lsqrt((M)/(2R(T_(L)-T_(0))))`

Answer

A

Explanation

`v=sqrt((gammaRT)/(M))=sqrt((5RT)/(3M))`
`dx=C.dt=sqrt((5R)/(3M)[T_(0)+((T_(L)-T_(0))/(L))x])dt`
`t=(2L)/(sqrt(T_(L))+sqrt(T_(0)))sqrt((3M)/(5R))`
`therefore (a)`