Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 35B / d / i / Solution

{c}

The Dieterici equation of state
$$
p=\frac{k_BT}{v-b}\exp\left(-\frac{a}{k_BTv}\right)
$$
models excluded volume through $b$ and attraction through $a$. Its critical point has $v_c=2b$ and $T_c=a/(4bk_B)$.


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