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Chapter 14: Problem 23

A thermometer containing \(0.10 \mathrm{g}\) of mercury is cooled from \(15.0^{\circ} \mathrm{C}\) to \(8.5^{\circ} \mathrm{C} .\) How much energy left the mercury in this process?

Short Answer

Expert verified
Answer: Approximately 0.091 Joules of energy leaves the mercury.

Step by step solution

01

Find the change in temperature

螖T = T_final - T_initial 螖T = 8.5掳C - 15.0掳C 螖T = -6.5掳C The negative sign indicates that the temperature decreased, which means that the mercury lost energy.
02

Find the specific heat capacity of mercury

The specific heat capacity of mercury (\(c\)) is a known value, which is approximately \(c = 140 \frac{\mathrm{J}}{\mathrm{kg}\cdot \mathrm{K}}\). Since the mass of mercury is given in grams, we need to convert the specific heat capacity to \(\frac{\mathrm{J}}{\mathrm{g} \cdot \mathrm{K}}\) by dividing by 1000: \(c = 0.14 \frac{\mathrm{J}}{\mathrm{g} \cdot \mathrm{K}}\)
03

Calculate the heat transfer (energy left)

Now we have all the values needed to solve for the heat transfer (\(Q\)) using the formula \(Q = mc螖T\): \(Q = (0.10 \thinspace \mathrm{g}) \cdot (0.14 \thinspace \frac{\mathrm{J}}{\mathrm{g} \cdot \mathrm{K}}) \cdot (-6.5 \thinspace \mathrm{K})\) \(Q = -0.091 \thinspace \mathrm{J}\) Since the value of \(Q\) is negative, it confirms that the energy left the mercury. In this process, approximately 0.091 Joules of energy left the mercury as it cooled from 15掳C to 8.5掳C.

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