(c) The output voltage of a thermocouple with the test junction at $t^{\circ} \mathrm{c}$ on gas thermometer scale and reference junction at ice point is given by $\varepsilon=0.19 t-5 \times 10^{-4} t^{2} \mathrm{mV}$. The millivoltmeter is calibrated at steam point and ice point. Determine the reading of this thermometer in a location where the gas thermometer reads $50^{\circ} \mathrm{C}$.
Explanation
The thermocouple output voltage is given by the equation $\varepsilon=0.19 t-5 \times 10^{-4} t^{2} \mathrm{mV}$. The millivoltmeter is calibrated at steam point and ice point, so we need to find the output voltage at steam point and ice point. The steam point is $100^{\circ} \mathrm{C}$ and ice point is $0^{\circ} \mathrm{C}$. We can find the output voltage at $50^{\circ} \mathrm{C}$ by substituting this value in the given equation. The reading of the thermometer is given by the ratio of the output voltage at $50^{\circ} \mathrm{C}$ to the output voltage at steam point.
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