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Chapter 14: Problem 54

The thermal resistance of a seal's fur and blubber combined is $0.33 \mathrm{K} / \mathrm{W} .\( If the seal's internal temperature is \)37^{\circ} \mathrm{C}\( and the temperature of the sea is about \)0^{\circ} \mathrm{C},$ what must be the heat output of the seal in order for it to maintain its internal temperature?

Short Answer

Expert verified
Answer: The heat output of the seal required to maintain its internal temperature at \(37^{\circ}\mathrm{C}\) is approximately \(112.12\,\text{W}\).

Step by step solution

01

The given values are: - Thermal resistance, \(R = 0.33 \mathrm{K} / \mathrm{W}\) - Seal's internal temperature, \(T_{in} = 37^{\circ}\mathrm{C}\) - Sea temperature, \(T_{out} = 0^{\circ}\mathrm{C}\) And the relationship between the heat output and thermal resistance is given by: \(Q = \frac{T_{in} - T_{out}}{R}\) #Step 2: Calculate the heat output (Q) by using the relationship and the given values#

Now we'll plug the given values into the relationship to calculate the heat output of the seal to maintain its internal temperature: \(Q = \frac{37^{\circ}\mathrm{C} - 0^{\circ}\mathrm{C}}{0.33\mathrm{K} / \mathrm{W}}\) #Step 3: Solve for Q#
02

Simplify and calculate the value of Q: \(Q = \frac{37\,\text{K}}{0.33\,\text{K/W}}\) \(Q \approx 112.12\,\text{W}\) #Step 4: State the result#

The heat output of the seal required to maintain its internal temperature at \(37^{\circ}\mathrm{C}\) is approximately \(112.12\,\text{W}\).

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Most popular questions from this chapter

A 10.0 -g iron bullet with a speed of $4.00 \times 10^{2} \mathrm{m} / \mathrm{s}\( and a temperature of \)20.0^{\circ} \mathrm{C}$ is stopped in a \(0.500-\mathrm{kg}\) block of wood, also at \(20.0^{\circ} \mathrm{C} .\) (a) At first all of the bullet's kinetic energy goes into the internal energy of the bullet. Calculate the temperature increase of the bullet. (b) After a short time the bullet and the block come to the same temperature \(T\). Calculate \(T\), assuming no heat is lost to the environment.
Five ice cubes, each with a mass of \(22.0 \mathrm{g}\) and at a temperature of \(-50.0^{\circ} \mathrm{C},\) are placed in an insulating container. How much heat will it take to change the ice cubes completely into steam?
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A tungsten filament in a lamp is heated to a temperature of $2.6 \times 10^{3} \mathrm{K}\( by an electric current. The tungsten has an emissivity of \)0.32 .$ What is the surface area of the filament if the lamp delivers $40.0 \mathrm{W}$ of power?
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