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Chapter 10: Problem 9

Does the amount of heat absorbed as \(1 \mathrm{~kg}\) of saturated liquid water boils at \(100^{\circ} \mathrm{C}\) have to be equal to the amount of heat released as \(1 \mathrm{~kg}\) of saturated water vapor condenses at \(100^{\circ} \mathrm{C}\) ?

Short Answer

Expert verified
Answer: Yes, the amount of heat absorbed during boiling of 1 kg of saturated liquid water and the heat released during condensation of the same amount of saturated water vapor are equal (approximately 2.26 * 10^6 Joules).

Step by step solution

01

Calculate the heat absorbed during boiling

We can calculate the heat absorbed during boiling using the latent heat of vaporization formula, which is: Q= m * L_v Where: Q = Heat absorbed during boiling in Joules m = mass of saturated liquid water (1 kg) L_v = latent heat of vaporization of water (approximately \(2.26\times10^6\) J/kg) Now we can plug in the values and calculate Q: Q = (1 kg) * (2.26 *10^6 J/kg) Q = 2.26 * 10^6 Joules So, the heat absorbed during boiling is approximately \(2.26\times10^6\) Joules.
02

Calculate the heat released during condensation

We can calculate the heat released during condensation using the latent heat of condensation formula, which is: Q = m * L_c Where: Q = Heat released during condensation in Joules m = mass of saturated water vapor (1 kg) L_c = latent heat of condensation of water (approximately \(2.26\times10^6\) J/kg, which is equal to latent heat of vaporization) Now we can plug in the values and calculate Q: Q = (1 kg) * (2.26 * 10^6 J/kg) Q = 2.26 * 10^6 Joules So, the heat released during condensation is approximately \(2.26\times10^6\) Joules.
03

Compare the two heat values

Now that we have calculated both heat values, we can compare them: Heat absorbed during boiling: 2.26 * 10^6 Joules Heat released during condensation: 2.26 * 10^6 Joules As we can see, the heat absorbed during the boiling of \(1 \mathrm{~kg}\) of saturated liquid water and the heat released during condensation of the same amount of saturated water vapor are equal. So yes, the amount of heat absorbed as \(1 \mathrm{~kg}\) of saturated liquid water boils at \(100^{\circ} \mathrm{C}\) has to be equal to the amount of heat released as \(1 \mathrm{~kg}\) of saturated water vapor condenses at \(100^{\circ} \mathrm{C}\).

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Most popular questions from this chapter

Saturated steam at \(30^{\circ} \mathrm{C}\) condenses on the outside of a 4-cm- outer-diameter, 2-m-long vertical tube. The temperature of the tube is maintained at \(20^{\circ} \mathrm{C}\) by the cooling water. Determine \((a)\) the rate of heat transfer from the steam to the cooling water, \((b)\) the rate of condensation of steam, and \((c)\) the approximate thickness of the liquid film at the bottom of the tube. Assume wavy-laminar flow and that the tube diameter is large, relative to the thickness of the liquid film at the bottom of the tube. Are these good assumptions?

10-59 The Reynolds number for condensate flow is defined as \(\operatorname{Re}=4 \dot{m} / p \mu_{l}\), where \(p\) is the wetted perimeter. Obtain simplified relations for the Reynolds number by expressing \(p\) and \(\dot{m}\) by their equivalence for the following geometries: \((a)\) a vertical plate of height \(L\) and width \(w,(b)\) a tilted plate of height \(L\) and width \(W\) inclined at an angle \(u\) from the vertical, \((c)\) a vertical cylinder of length \(L\) and diameter \(D,(d)\) a horizontal cylinder of length \(L\) and diameter \(D\), and (e) a sphere of diameter \(D\).

Water is to be boiled at sea level in a 30 -cm-diameter mechanically polished AISI 304 stainless steel pan placed on top of a \(3-\mathrm{kW}\) electric burner. If 60 percent of the heat generated by the burner is transferred to the water during boiling, determine the temperature of the inner surface of the bottom of the pan. Also, determine the temperature difference between the inner and outer surfaces of the bottom of the pan if it is 6-mm thick. Assume the boiling regime is nucleate boiling. Is this a good assumption?

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A 65 -cm-long, 2-cm-diameter brass heating element is to be used to boil water at \(120^{\circ} \mathrm{C}\). If the surface temperature of the heating element is not to exceed \(125^{\circ} \mathrm{C}\), determine the highest rate of steam production in the boiler, in \(\mathrm{kg} / \mathrm{h}\).
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