Question

The sketch shows the plot of Z v/s P for a hypothetical gas for one mole at three distinct temperature . Boyle's temperature is the temperature at which a gas shows ideal behavior over a pressure range in the low-pressure region .Boyle's temperature $\left(T_b\right)$= $\frac{a}{Rb}$.If a plot is obtained at temperatures 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 $C{O}_2$ and the temperature well above critical temperature curve is more like $H_2$ at $O^0$ C as shown above.At high pressure suppose all the constant temperature curve varies linearly with pressure according to the following equation $Z=1+\frac{Pb}{RT}(R=2calmo{l}^{-1}{K}^{-1}$)

Which of the following is correct?

• A. $\frac{a}{b}<0.4kcalmo{l}^{-1}$
• B. 0.4 k cal $mo{l}^{-1}<\frac{a}{b}<2kcalmo{l}^{-1}$
• C. $\frac{a}{b}>0.4kcalmo{l}^{-1}$
• D. $\frac{a}{b}=1Kcalmo{l}^{-1}$

Answer 1

The correct option is B 0.4 k cal $mo{l}^{-1}<\frac{a}{b}<2kcalmo{l}^{-1}$

As given,
200 < $T_B$ < 1000
$\to 200<\frac{a}{Rb}$ < 1000
$\to 400cal<\frac{a}{b}$< 2000 cal
$\to 0.4kcalmo{l}^{-1}<\frac{a}{b}<2kcalmo{l}^{-1}$