Thermometer

Immerse a thermometer with a heat capacity of 2.0 J. K-1 in water weighing 67.0 grams. Before immersion in water, the thermometer showed a temperature of 17.8 degrees Celsius. After reaching equilibrium, the temperature is 32.4 degrees. What was the water temperature before the measurement?

Correct answer:

t =  32.505 °C

Step-by-step explanation:

$$\begin{gathered} m=67\text{ g } \\ C=2.0\text{ J/K } \\ {c}_1=4.180\text{ J/g/K } \\ {t}_1=17.8\text{ °C } \\ {t}_2=32.4\text{ °C } \\ t>t_2>t_1 \\ m\cdot c_1\cdot (t-t_2)=C\cdot (t-t_1) \\ 67\cdot 4.18\cdot (t-32.4)=2\cdot (t-17.8) \\ 278.06t=9038.344 \\ t=32.505013=32.505\text{°C} \end{gathered}$$

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