Is it possible to deduce the second law of thermodynamics from the first? Considering the First law of thermodynamics as an axiom dU=dQ-pdV for any infinitesimal process, we should be able to prove that for any reversible(quasistatic) and cyclic transformation, there is at least one part in the transformation such that dQ<0. So there exists a part in the cycle in which the engine loses heat. 
As the efficiency for the cycle is defined as e=1-(Qout\Qin)  it follows that e<1. But this is in fact the Kelvin-Planck statement of the Second law for reversible processes! Thus (for quasistatic processes at least) shouldn't this be considered a theorem, rather than an axiom/postulate?
 A: The first law is about conservation of energy.
The second law is about irreversibility of processes if this involved decreasing entropy in a closed system.
If there are say $N$ degrees of freedom in a system that can be excited, then distributing a given amount of energy $E$ only on say one state (low entropy) of the $N$ or randomly over many of them (high entropy) would both be conserving the energy $E$. So thermodynamically going from a state with high entropy to a state with low entropy concentrating the same amount of energy on few degrees of freedom is not violating the first law. It is however violating the second law in the following sense: going from a high entropy state to such a highly ordered state is extremely unlikely and hence not going to happen in a thermodynamic limit.
Hence the second law of thermodynamics adds new information that cannot be derived from the first one.
A: you have to prove e < 1 for all processes including irreversible processes to prove second law. your line of reasoning has nothing to say about irreversible changes. this is my first reaction. i too have been thinking about this for a long time. for another perspective, see my book 'The principles of thermodynamics' N.D. Hari Dass.
there is a flaw in my argument there proving equivalence of entropy axiom and second law, which has to do precisely with irreversible engines.
