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)`)
For 500 K plot value of Z changes from 2 to 2.2 if pressure is varied from 1000 atm to 1200 atm (high pressure ) then the value of `b/(RT)` will be

Options

A. `10^(-3) "atm"^(-1)`
B. `2xx10^(-3) "atm"^(-1)`
C. `5xx10^(-4) "atm"^(-1)`
D. `10^(-4) "atm"^(-1)`

Answer

A

Explanation

We know that, in the high pressure region `z=1+(Rb)/(RT)`
solve this equation for the two points and get result (value of `b/(RT)`)