For one mole of a real gas

PHYSICS · Subjective · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

For one mole of a real gas, a simplified form of the Van der Waals equation is written as

\Bigl(p+\frac{a}{V^{2}}\Bigr)(V-b)=RT,

where

p

is pressure,

V

is molar volume,

T

is absolute temperature,

R

is the universal gas constant, and

a

and

b

are empirical constants. (i) Show by dimensional reasoning that the product

pV

has the same dimensions as

RT

. (ii) Determine the dimensions of the constant

a

so that the term

a/V^{2}

is compatible with pressure. (iii) Determine the dimensions of the constant

b

so that

(V-b)

can be algebraically combined with

V

. (iv) Using your results, explain why the form

(p+ a/V^{2})(V-b)=RT

satisfies the requirement of dimensional homogeneity.