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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

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.
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 \(Q = mcΔT\): \(Q = (0.10 \thinspace \mathrm{g}) \cdot (0.14 \thinspace \frac{\mathrm{J}}{\mathrm{g} \cdot \mathrm{K}}) \cdot (-6.5 \thinspace \mathrm{K})\) \(Q = -0.091 \thinspace \mathrm{J}\) 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.

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Most popular questions from this chapter

A blacksmith heats a 0.38 -kg piece of iron to \(498^{\circ} \mathrm{C}\) in his forge. After shaping it into a decorative design, he places it into a bucket of water to cool. If the available water is at \(20.0^{\circ} \mathrm{C},\) what minimum amount of water must be in the bucket to cool the iron to \(23.0^{\circ} \mathrm{C} ?\) The water in the bucket should remain in the liquid phase.
An \(83-\mathrm{kg}\) man eats a banana of energy content $1.00 \times 10^{2} \mathrm{kcal} .$ If all of the energy from the banana is converted into kinetic energy of the man, how fast is he moving, assuming he starts from rest?
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For a cheetah, \(70.0 \%\) of the energy expended during exertion is internal work done on the cheetah's system and is dissipated within his body; for a dog only \(5.00 \%\) of the energy expended is dissipated within the dog's body. Assume that both animals expend the same total amount of energy during exertion, both have the same heat capacity, and the cheetah is 2.00 times as heavy as the dog. (a) How much higher is the temperature change of the cheetah compared to the temperature change of the dog? (b) If they both start out at an initial temperature of \(35.0^{\circ} \mathrm{C},\) and the cheetah has a temperature of \(40.0^{\circ} \mathrm{C}\) after the exertion, what is the final temperature of the dog? Which animal probably has more endurance? Explain.
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