If for hydrogen `C_(P) - C_(V) = m` and for nitrogen `C_(P) - C_(V) = n`, where `C_(P)` and `C_(V)` refer to specific heats per unit mass respectively at constant pressure and constant volume, the relation between `m` and `n` is (molecular weight of hydrogen = 2 and molecular weight or nitrogen = 14)

Options

A. n = 14m
B. n = 7m
C. m = 7n
D. m = 14m

Answer

A

Explanation

At t = 0 particle is at origin (x = 0) potential energy at origin (x = 0) = 15 J
`therefore` total mechanical energy `=K.E+P.E=(1)/(2)xx2(4sqrt(6))^(2)+15=96+15=111J`
`because U=-x^(3)+6x^(2)+15`
`(du)/(dx)=-3x^(2)+12x`
`0=-3x(x-4)`
`x=0" and "x=4, " since "F=-(du)/(dx)`
therefore force on particle is zero at x = 4
Potential energy at (x = 4) = 47 J
By conservation of mechanical energy
`M.E=K.E+P.E.implies111=47+K.EimpliesV=8ms^(-1)`