Question

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

Answer: Approximately 0.091 Joules of energy leaves the mercury.

Step-by-step solution

Find the change in temperature

ΔT = T_final - T_initial ΔT = 8.5°C - 15.0°C ΔT = -6.5°C The negative sign indicates that the temperature decreased, which means that the mercury lost energy.

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: \(c = 0.14 \frac{\mathrm{J}}{\mathrm{g} \cdot \mathrm{K}}\)

Calculate the heat transfer (energy left)

Now we have all the values needed to solve for the heat transfer (\(Q\)) using the formula \(Q = mcΔT\): \(Q = (0.10 \thinspace \mathrm{g}) \cdot (0.14 \thinspace \frac{\mathrm{J}}{\mathrm{g} \cdot \mathrm{K}}) \cdot (-6.5 \thinspace \mathrm{K})\) \(Q = -0.091 \thinspace \mathrm{J}\) 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°C to 8.5°C.