(d) In part (c) we found the dependence of the lifetime on the fundamental constants. This is independent of nuclear reaction rates so it appears that a deuterium composition would make no difference. However, this cannot be so simple since the same argument would show also that the Sun's lifetime would be the same even if there were no nuclear reactions! (Set all the rates to zero and observe the equation is unchanged.) We have clearly assumed that an equilibrium is possible in which nuclear reactions can provide the solar luminosity under the conditions in the centre. We can accept this is true for the actual Sun, so it is true also for a deuterium Sun since increasing the reaction rates makes things easier. Thus the lifetime would indeed be unchanged, but the radius would increase reducing the central temperature and bringing the reaction rates down into line with the flux of radiant energy.