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Byju's Answer

Standard XII

Physics

Conduction Law

The gas equat...

Question

The gas equation for $n$ moles of a real gas is $(P + \frac{a}{V^{2}}) (V - b) = n R T$ , where $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature, $R$ is the molar gas constant and $a, b$ are arbitrary constants. Which of the following have the same dimensions as those of $P V$ ?

n R T

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\frac{a}{V}

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P b

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\frac{a b}{V^{2}}

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Solution

The correct option is D $\frac{a b}{V^{2}}$

$(P + a / V^{2}) (V - b) = n R T \Rightarrow [P] = [a / V^{2}] a n d [V] = [b] \Rightarrow [P] [V] = [a / V^{2}] [V] \Rightarrow [P V] = [a / V] S i m i l a r l y \Rightarrow [P V] = [P] [b] [P] = [a / V^{2}] a n d [V] = [b] \Rightarrow [P] [V] = [a / V^{2}] [b]; \Rightarrow [P] [V] = [a b / V^{2}]$

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The gas equation for n moles of a real gas is (P+aV2)(V−b)=nRT, where P is the pressure, V is the volume, T is the absolute temperature, R is the molar gas constant and a,b are arbitrary constants. Which of the following have the same dimensions as those of PV ?

The correct option is D abV2 (P+a/V2)(V−b)=nRT⇒[P] =[a/V2] and [V]=[b]⇒[P] [V]=[a/V2][V]⇒[PV]=[a/V]Similarly ⇒[PV]=[P][b][P] =[a/V2] and [V]=[b]⇒[P] [V]=[a/V2][b] ; ⇒[P] [V]=[ab/V2]