Question

10. A thermocouple recorded an e.m.f. of 8.00 mV when it is in
melting ice and 24.0 mV when it is in boiling water.
When it is placed in a hot melting metal , it recorded
an e.m.f. of 56 mV.
What is the temperature of the melting metal ?

A. 233 °C B. 300 °C C. 920°C D. 1020 °C

Answer 1

In a typical thermocouple, the voltage is linearly dependent from the temperature[1]. If the voltage rises from 8 mV (melting ice, 0 °C) to 24 mV (boiling water, 100 °C), the voltage will rise
\[\frac{(24-8) \mathrm{mV}}{100\mathrm{°C}}=0.16\frac{\mathrm{mV}}{\mathrm{°C}}\]

Therefore, the voltage increase of 56 mV - 8 mV = 48 mV equals to temperature increase of 48/0.16=300 degrees, which is the final answer (option B).

[1] http://en.wikipedia.org/wiki/Thermocouple#Voltage.E2.80.93temperature_relationship