For one mole of a Vander Waal-s gas when b -0 and T -300 K- the PV vs- 1- V plot is shown below- The value of the vander waal-s constant -a- atm L 2 mol -2A- 3B- 4-5C- 1D- 1-5

The correct option is D 1.5The vanderwaal's equation of state is ( P+n^2 a/V^2 ) (V nb) = nRT For one mole and when b = 0, the above equation condenses to ( ...

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Standard XII

Physics

Real Gas Equation

For one mole ...

Question

For one mole of a Vander Waal’s gas when b = 0 and T = 300K, the PV vs. $\frac{1}{V}$ plot is shown below. The value of the vander waal's constant ‘a’ $(a t m L^{2} m o l^{- 2})$

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4.5

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1.5

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Solution

The correct option is C 1.5
The vanderwaal's equation of state is
$(P + \frac{n^{2} a}{V^{2}}) (V - n b) = n R T$
For one mole and when b = 0, the above equation condenses to
$(P + \frac{n^{2} a}{V^{2}}) V = R T \Rightarrow P V = R T - \frac{a}{V}$ . . . . .(i)
Equation (i) is a straight line equation between PV and $\frac{1}{V}$ whose slope is '- a'. Equating with slope of the straight line given in the graph
$- a = \frac{20.1 - 21.6}{3 - 2} = - 1.5 \Rightarrow a = 1.5$

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For one mole of a Vander Waal’s gas when b = 0 and T = 300K, the PV vs. 1V plot is shown below. The value of the vander waal's constant ‘a’ (atm L2mol−2)

For one mole of a Vander Waal’s gas when b = 0 and T = 300K, the PV vs. $\frac{1}{V}$ plot is shown below. The value of the vander waal's constant ‘a’ $(a t m L^{2} m o l^{- 2})$