Chapter 16: Problem 6
Why do large bodies of water exert a temperature-moderating effect on their surroundings?
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Chapter 16: Problem 6
Why do large bodies of water exert a temperature-moderating effect on their surroundings?
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A blue giant star whose surface temperature is 23 kK radiates energy at the rate of \(3.4 \times 10^{30} \mathrm{W}\). Find the star's radius, assuming it bchaves like a blackbody.
You arrive for a party on a night when it's \(8^{\circ} \mathrm{C}\) outside. Your hosts meet you at the door and say the party may need to be cancelled, because the heating system has failed and they don't want to discomfort their guests. You say, "Not so fast!" A total of 36 people are expected, the average power output of a human body is \(100 \mathrm{W},\) and the house loses energy at the rate \(320 \mathrm{W} / \mathrm{C} .\) Will the house remain comfortable?
Find the \(\mathcal{R}\) -factor for a wall that loses 0.040 Btu each hour through each square foot for each \(^{\circ} \mathrm{F}\) temperature difference.
Your young niece complains that her cocoa, at \(90^{\circ} \mathrm{C},\) is too hot. You pour 2 oz of milk at \(3^{\circ} \mathrm{C}\) into the 6 oz of cocoa. Assuming milk and cocoa have the same specific heat as water, what's the cocoa's new temperature?
A more realistic approach to the solar greenhouse of Example 16.7 considers the time dependence of the solar input. A function that approximates the solar input is \(\left(40 \mathrm{Btu} / \mathrm{h} / \mathrm{ft}^{2}\right) \sin ^{2}(\pi t / 24)\) where \(t\) is the time in hours, with \(t=0\) at midnight. Then the greenhouse is no longer in energy balance, but is described instead by the differential form of Equation 16.3 with \(Q\) the timevarying energy input. Use computer software or a calculator with differential-equation-solving capability to find the time-dependent temperature of the greenhouse, and determine the maximum and minimum temperatures. Assume the same numbers as in Example 16.7 , along with a heat capacity \(C=1500 \mathrm{Btu} /^{\circ} \mathrm{F}\) for the greenhouse. You can assume any reasonable value for the initial temperature, and after a few days your greenhouse temperature should settle into a steady oscillation independent of the initial value.
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