12.2 On the basis of the following information, which is partly hypothesis and partly somewhat simplified experimental data, calculate the melting pressure of \( { }^{3} \mathrm{He} \) at \( 0 \mathrm{~K} \).
(a) Between 0 and \( 10 \mu \mathrm{K} \), the heat capacity of the solid is very high, but between \( 10 \mu \mathrm{K} \) and \( 1 \mathrm{~K} \), it is much less than that of the liquid.
(b) Below \( 1 \mathrm{~K} \) the heat capacity of the liquid is proportional to \( T \).
(c) The expansivity of both phases may be assumed to be zero.
(d) At \( 0.4 \mathrm{~K} \), the melting pressure \( p_{\mathrm{m}} \) is \( 30 \mathrm{~atm} \) and \( \mathrm{d} p_{\mathrm{m}} / \mathrm{d} T=0 \). At \( 0.7 \mathrm{~K} \), \( p_{\mathrm{m}} \) is \( 33 \mathrm{~atm} \).
