Which of the following parameters correctly represent conditions for a spontaneous process with no non P-V work involved?

(P) $(dH{)}_{S.P}<0$

(Q) $(dU{)}_{S,P}<0$

(R) $(dG{)}_{T,V}<0$

(S) $(dH{)}_{P,T}>0$

(T) $(dS{)}_{\text{universe }}>0$

(U) $(dS{)}_{U,V}>0$

The TDS equations given as,

$\begin{array}{l}dH=TdS+Vdp\\ dU=TdS-pdV\\ dG=-SdT+VdP\\ dS=\frac{dU}{T}+P\frac{dV}{T};U=f(S,V);H=f(S,P);G=f(T,P)\end{array}$

$(dS{)}_{\text{universe }}>0$ for process to be spontaneous.

To write the differential expression for any of these functions in terms of the differentials of its natural independent variables, we need only to note that the coefficient of the differential of independent variable is placed diagonally opposite this variable on the square. An arrow pointing away from a natural variable indicates a +ve sign.