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  •  Which of the following statements of real gas are correct? I. langer the <img alt="\mathrm{\frac{T_e}{P_c}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cfrac%7B

 Which of the following statements of real gas are correct?
I. langer the \mathrm{\frac{T_e}{P_c}} value of a gas, langer would be the excluded volume (b)
II. If \mathrm{\left(\frac{a b}{v^2}\right) } in negligible the second virial co-cefficient B in the viral equation is \mathrm{ \left(b-\frac{a}{K T}\right) }
III. At Boyle's temperature the coefficient B is zero.
Select the cored answers using the codes given below -
 

Option: 1

 Both I. II


Option: 2

 Both I, III
 


Option: 3

 I, II and III


Option: 4

 None of these


Answers (1)

best_answer

\\\mathrm{I.~ \frac{T_c}{P_c}=\frac{8 a}{27 Rb} \times \frac{27 b^2}{a}=\frac{8 b}{R} \\ Thus \frac{T_c}{P_c} \alpha \text{ b thus correct.} }


\begin{aligned} \mathrm{II~}&\mathrm{ \frac{P_c}{27 P b} }\\ &\mathrm{ \left(P+\frac{a}{V^2}\right)(V-b)=R T \Rightarrow P V+\frac{a}{V}-\frac{a b}{V^2}-P b=R T} \\ & \mathrm{\Rightarrow P V=R T+P b-\frac{a}{V}=R T+\frac{R T}{V} b-\frac{a}{V}} \\ &\mathrm{ =R T\left[1+\frac{1}{V}\left(b-\frac{a}{R T}\right)\right] }\\ &\mathrm{ P V=R T\left[1+\frac{B}{V}+\cdots\right]}\\ &\text{on comparison with } \mathrm{P V=R T\left[1+\frac{B}{V}+\cdots\right]}\\ &\mathrm{B=\left(b-\frac{a}{R T}\right) \text { ic cared. } } \end{aligned}

\mathrm{III.~ When T=\frac{a}{R b} }\text{(Boyle's temperature) Then B}=\mathrm{\left(b-\frac{a}{R g / R b}\right)=0}

 

Posted by

himanshu.meshram

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