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The equation of a state of a real gas is...

The equation of a state of a real gas is given by `(P + (a)/(V^(2))) (V - b) = RT`, where `T` is absolute temperature, `P` is pressure, `V` is volume and `R` is universal gas constant. What are the dimensions of constant `a` and `b` ?

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To find the dimensions of constants \( a \) and \( b \) in the given equation of state for a real gas, we will analyze the equation step by step. ### Given Equation: \[ (P + \frac{a}{V^2})(V - b) = RT \] ### Step 1: Analyze the Terms ...
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Knowledge Check

  • The equation of state for a real gas is given by (P+(a)/(v^(2)))(v-b)=RT the dimensions of constant a are

    A
    `[ M L^(5) T^(–2)]`
    B
    `[ M^(–1) L^(5) T^(2)]`
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    D
    `[ M L^(5) T^(–1)]`

  • The equation of state of some gases can be expressed as (P+ (a)/(V^(2)))(V-b)= RT , where P is the pressure, V is the volume, T is the absolute temperature and a, b & R are constants. The dimensions of 'a' are : -

    A
    `[ML^(5)T^(-2)]`
    B
    `[ML^(-1)T^(-2)]`
    C
    `[L^(3)]`
    D
    `[L^(6)]`

  • The equation fo state of a gas is given by (P+(a)/(V^(3)))(V-b^(2))=cT , where P,V,T are pressure, volume and temperature respectively, and a,b,c are constants. The dimesions of a and b are respectively

    A
    `[ML^(8)T^(-2)] and [L^(3//2)]`
    B
    `[ML^(5)T^(-2)] and [L^(3)]`
    C
    `[ML^(5)T^(-2)] and [L^(6)]`
    D
    `[ML^(6)T^(-2)] and [L^(3//2)]`

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