# Nernst Calculators

The Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half cell or full cell reaction) to the standard electrode potential. In this application, the Nernst equation is used to calculate the partial pressure (concentration) of oxygen. The equation relies upon temperature and mV reading to provide the oxygen concentration with respect to the reference air concentration (20.9%). $$E=\frac{RT}{4F}ln\left(\frac{pO_{2}}{pO'_{2}}\right)$$ Where:

E = sensor electromotive force, (mV)

R = gas constant 8.3145 JK-1mol-1

T = temperature, (Kelvin)

n = number of charges per reactant species

F = Faraday's constant 96485 C mol-1

p = partial pressure (mole fraction)

The calculators below will allow you to calculate the oxygen concentration from the SIRO 2 sensor signal, or the mV for a given oxygen concentration.

### Concentration Calculator

Please enter the operating temperature (500 - 1700 °C) and the measured mV (0 - 1200 mV) signal. The corresponding oxygen concentration is calculated. If it is very low, it is displayed in scientific notation.

If oxygen is to be measured, using an oxygen probe and atmospheric air, with $$pO_2 = 0.209$$ as a reference, this equation simplifies to:
$$pO_2^{\prime}=pO_2e^{-E\frac{4F}{RT}}$$

### Nernst mV Calculator.

The equation may be re-arranged, to allow calculation of the emf from a known reference concentration and a measured oxygen concentration:
$$E=0.0496T \ln\left( \frac{pO_2}{pO_2^{\prime}} \right)$$

This calculator will allow the calculation of the expected Nernst voltage given specific temperature and oxygen values. Note that the oxygen concentration can be entered either as a decimal fraction (so that 1% would be entered as 0.01) or in power of 10 notation ( so that 0.001% would be 1.00*10^-5).

# Carbon Potential Calculators

The carbon calculators here provide the user the following:

• Carbon potential as a function of oxygen sensor millivolt and temperature;
• Partial pressure of O2 (mV) as a function of carbon potential and temperature;
• Temperature as a function of carbon potential and partial pressure of oxygen in millivolts;
• Carburizing time for a given depth, or depth for a given time of carburizing.

## What is Carbon Potential

The carbon potential of a furnace atmosphere at a specified temperature is defined as the carbon content of pure iron that is in thermodynamic equilibrium with the atmosphere. The carbon potential of the furnace atmosphere must be greater than the carbon potential of the surface of the workpieces in order for carburizing to occur. (Stickels, 1991)

Schmidt writes that carbon potential is defined as the equilibrium carbon level in the austenite that is obtained for a given temperature and ratio of CO and CO2 gases (Schmidt, 1990).

## How is Carbon Potential Created and Calculated

The carbon activity of the atmosphere or the steel can be predicted by equilibrium calculations. It is defined as the carbon content, expressed in weight per cent, that an initially pure iron specimen would have if carbon is equilibrated between the atmosphere or the alloy under consideration. In practical heat treatment it is common to apply the so-called carbon potential rather than the carbon activity (Hack, K, 2008, p 212).

## References

Hack, K. (2008). Sgte Casebook: thermodynamics at work. Woodhead Pub.

Blumenthal, R. N. (1995). A Technical Presentation of the Factors Affecting the Accuracy of Carbon/Oxygen Probes. Proceedings of the Second International Conference on Carburizing and Nitriding with Atmospheres, 17–22.

Schmidt, M. L. (1990). Preoxidation Prior to Gas Carburizing: Theory and Its Effect on Pyrolwear(R) 53 Alloy. J. Heat Treating, 8(1), 5–19.

Stickels, C. A. (1991). Gas Carburizing of Steels. In ASM Handbook Vol. 4 : Heat Treating (p. 728). ASM International.