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Standard XII

Chemistry

Van der Waal's Equation - Derivation

The Van der W...

Question

The Van der Waals equation of state is $(p + \frac{a}{v^{2}}) (v - b) = R T$ , where \9p\) is pressure, $v$ is specific volume, $T$ is temperature and $R$ is characteristic gas constant. The $S I$ unit of $a$ is

J / k g K

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P a / k g

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m^{5} / k g - s^{2}

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m^{3} / k g

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Solution

The correct option is C $m^{5} / k g - s^{2}$
The Vander waals equation,

$(p + \frac{a}{v^{2}}) (v - b) = R T$

According to the equation, the unit of pressure and $(a / v^{2})$ should be the same.

$∴$ $Unit of p = Unit of \frac{a}{v^{2}}$

$\frac{k g}{m - s e c^{2}} = \frac{(k g)^{2} \times a}{m^{6}}$

$a = m^{5} / k g - s e c^{2}$

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The Van der Waals equation of state is (p+av2)(v−b)=RT, where \9p\) is pressure, v is specific volume, T is temperature and R is characteristic gas constant. The SI unit of a is

The correct option is C m5/kg−s2The Vander waals equation, (p+av2)(v−b)=RT According to the equation, the unit of pressure and (a/v2) should be the same. ∴ Unit ofp= Unit of av2 kgm−sec2=(kg)2×am6 a=m5/kg−sec2

The Van der Waals equation of state is $(p + \frac{a}{v^{2}}) (v - b) = R T$ , where \9p\) is pressure, $v$ is specific volume, $T$ is temperature and $R$ is characteristic gas constant. The $S I$ unit of $a$ is