Question

Sketch shows the plot of $Z$ vs $p$ for a hypothetical gas for one mole at three distinct temperature

Boyle's temperature is the temperature at which a gas shows ideal behaviour over a pressure range in the low pressure region. Boyle's temperature $\left(T_b\right)=\frac{a}{R b}$. If a plot is obtained at temperature 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 above critical temperature curve is more like $H _2$ at $0^{\circ} C$
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 $\frac{b}{R T}$ will be

• A. $10^{-4}\, atm ^{-1}$
• B. $10^{-3} \,atm ^{-1}$
• C. $10^{-5} \,atm ^{-1}$
• D. $0.10 \,atm ^{-1}$

Answer 1

Answer: (B)

We know that
In the high pressure region
$Z=1+\frac{p b}{R T}$
$2=1+\frac{1000 b}{R T} \ldots \text { (i) }$
$2.2=1+\frac{1200 b}{R T} \ldots \text {..ii) }$
Solving both the equation we get $\frac{b}{R T}=10^{-3} atm ^{-1}$