Sketch shows the plot of Z v/s P for a hypothetical gas for one mole at three distint temperature.

Boyle's temperature is the temperature at which gas shows ideal behaviour over a pressure range in the low pressure region.Boyle's temperature `(T_b)=a/(Rb)`.If a plot is obtained at temperature well below Boyle's temperature then the curve will show negative deviation, in low pressure region and positive deviation in the high pressure region. Near critical temperature the curve is more likely as `CO_2` and the temperature well above critical temperature curve is more like `H_2` at `0^@C` as shown above.At high pressure suppose all the constant temperature curve varies linearly with pressure according to the following equation : `Z=1+(Pb)/(RT)` (`R=2 cal "mol"^(-1) K^(-1)`)
Which of the following is correct :

Options

A. `a/b lt 0.4 k cal mol^(-1)`
B. 0.4 k cal `"mol"^(-1) lt a/b lt 2` k cal `"mol"^(-1)`
C. `a/b lt 0.4 k cal mol^(-1)`
D. `a/b =1 K Cal "mol"^(-1)`

Answer

B

Explanation

`200ltT_blt1000`
`implies 20lta/(Rb)lt1000implies 400 cal lt a/b lt 2000 cal`