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If the equation of state of a gas isexpressed as (P+(a)/(V^(2)))(V-b)=RT where Pis the pressure V is the volume and T the absolute temperature and a,b,R are cosntants then find the dimensions of a and b . |
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Answer» Solution :By principle of homogeneity of dimensions P can added to P only. ITMEANS `(a)/(V^(2))` also gives pressure. Dimension formulae for pressure (P) =` M^(1)L^(-1)T^(-2)` and Volume (V) =` M^(0)L^(3)T^(0)` . Since `(a)/(V^(2)) ` = pressure `:.(a)/((M^(0)L^(3)T^(0))^(2))=M^(1)L^(-1)T^(-2)IMPLIES (a)/(M^(0)L^(6)T^(0))=M^(1)L^(-1)T^(-2)` `:. a = M^(1)L^(5)T^(-2)` Similarly b will have same dimension as volume V-b = volume `:. b = M^(0)L^(3)T^(0)` |
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