Question

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

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

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#

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 \(112.12\,\text{W}\).