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Real Gases

For 500 K p...

Question

For $500 K$ plot value of $Z$ changes from $2$ to $2.2$ if pressure is varied from $1000 a t m$ to $1200 a t m$ (high pressure) then the value of $\frac{b}{R T}$ will be:

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Solution

$Slope for Z versus P graph is \frac{b}{R T} Z = 1 + \frac{P b}{R T} = c + P (s l o p e) \Rightarrow S l o p e = \frac{Z_{2} - Z_{1}}{P_{2} - P_{1}} = \frac{2.2 - 2}{1200 - 1000} = \frac{0.2}{200} = 10^{- 3} = 0.001$

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Q. For 500K plot the 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:

Q. 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}

Q. The sketch shows the plot of Z vs P for 1 mole of a hypothetical gas at three distinct
temperatures:

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

(T_{b}) = \frac{a}{R b}

. If a plot is
obtained at temperatures well below Boyle's temperature, then the curve will show a negative deviation in the low pressure region and a positive deviation in the high pressure
region.

In the first figure, in the plot at

500 K, Z

changes from 2 to 2.2 as the pressure varies from 1000 atm to

1200 atm

(high pressure). The value of

\frac{b}{R T}

The sketch shows the plot of

Z

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

(T_{b})

\frac{a}{R b}

.If a plot is obtained at temperatures well below Boyle's temperature then the curve will show negative deviation, in the 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}

O^{o} 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{P b}{R T} (R = 2 c a l m o l^{- 1} K^{- 1}

)

K

Z

changes from 2 to 2.2 ,if pressure is varied from 1000

a t m

a t m

(high pressure) then the value of

\frac{b}{R T}

Q. The sketch shows the plot of Z vs P for 1 mole of a hypothetical gas at three distinct
temperatures:

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

(T_{b}) = \frac{a}{R b}

. If a plot is
obtained at temperatures well below Boyle's temperature, then the curve will show a negative deviation in the low pressure region and a positive deviation in the high pressure
region.

In the first figure, in the plot at

500 K, Z

changes from 2 to 2.2 as the pressure varies from 1000 atm to

1200 atm

(high pressure). The value of

\frac{b}{R T}

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