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Questions  >>  CBSE XI  >>  Physics
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Q)

If $\bigg(p+\large\frac{a}{v^2}\bigg)$$(v-b)=RT$</br>$where\; P=pressure,V=volume,R=gas \;constant, T=temperature$ <br>Then find dimension of a and b?

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A)
Solution :
$(P + a/V_2) (V - b) = RT$
P is pressure, V is volume and T is temperature.
$[P] = [F/A] = [MLT _2/L_2] = [ML_1T_2]$
$[V]=[L_3]$
We cannot add or subtract quantities of different dimensions.
Therefore $[P] = [a/V_2] ⇒ [a] = [PV_2] = [ML_1T_2 L_6] = [M L_5 T_2]$
$\therefore [a]=[ML_5T_2]$
Similarly, $[b] = [V] = [L_3]$
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