What will be the relation between the `T_(1)` of gas 1 with `M_(1)=56` and `T_(2)` of gas 2 with `M_(2)=44` if the average speed of gas 1 is equal to most probable speed of gas 2?

Options

A. `T_(1)=T_(2)^(2)`
B. `T_(1)=T_(2)`
C. `T_(1)=(T_(2))^(1//2)`
D. `T_(1)=1//T_(2)`

Answer

B

Explanation

`C_(RV)=sqrt((8RT)/(piM))and C_(mp)=sqrt((2RT)/(M))`
Now `C_(av)(" gas 1")=C_(mp)("gas 2")`
`sqrt((8RT_(1))/(piM_(1)))=sqrt((2RT_(2))/(M_(2)))`
`(8T_(1))/(piM_(1))=(2T_(2))/(M_(2)) or (4T_(1))/(pixx56)=(T_(2))/(44)`
`therefore" "(T_(1))/(T_(2))=(56xxpi)/(44xx4)=(56xx3.142)/(44xx4)=1`
`therefore " "T_(1)=T_(2)`