The bulk modulus of a substance is the ratio of a small decrease in pressure to the resulting fractional increase in volume: d p dv show that b (5/3) p, in the free electron gas model, and use your result in problem 521 (d) to estimate the bulk modulus of copper. comment: the observed value is 13.4 × 100 n/m2, but don't expect perfect agreement-after all, we're neglecting all electron- nucleus and electron electron forces! actually, it is rather surprising that this calculation comes as close as it does.