# In the Nernst equation, does T refer to the temperature of the standard cell or the cell under non-standard conditions?

I am doing an experiment where I am varying the temperature of the electrolyte of the anode half cell. I am trying to calculate the cell potential using the Nernst equation under standard conditions but I'm not sure what T to put in.

• Think of the Nernst equation as the electrochemical analog of the equilibrium expression in terms of Gibbs functions, so it refers to a constant T. The T you put into the equation should be that of the reference conditions. The equation refers to a process at constant T: T and $E^0$ refer to the same T. – Buck Thorn Dec 8 '18 at 13:00

The Nernst equation is $$\displaystyle E=E^\text{o}-\frac{RT}{nF}\ln(Q)$$ where $$Q$$ is the ratio of activities, $$a$$, of products over reactants, e.g. for $$aA+B\leftrightharpoons cC+D$$ then $$\displaystyle Q=\frac{a^c_Ca_D}{a^a_Aa_B}$$. The emf of the cell is $$E^\text{o}$$ which is measured when the emf of the cell is zero, $$E=0$$, no current flows, and means that the reactants and products are at equilibrium. In this case $$\displaystyle E^\text{o} =\frac{RT}{nF}\ln(K_e)$$ where $$K_e$$ is the equilibrium constant.
The measured emf $$E$$ changes with temperature as indicated by the Nernst equation and this is a good way to measure thermodynamic properties; for example the reaction free energy is $$\Delta G = -nFE$$ and because $$\partial\Delta G/\partial T|_p=-\Delta S$$ then $$\displaystyle \Delta S = \frac{\partial E}{\partial T}\bigg|_p nF$$ which is a convenient way to determine the entropy change in a reaction by measuring the reaction emf at two temperatures and letting the derivative be $$\Delta E/\Delta T$$, which will be accurate for a small change in temperature, and give $$\Delta S$$ at the mean of the two temperatures. Since $$\Delta G = \Delta H -T\Delta S$$ the change in enthalpy can also be calculated.