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Chapter 11: Problem 166

Saturated water vapor at \(40^{\circ} \mathrm{C}\) is to be condensed as it flows through the tubes of an air-cooled condenser at a rate of \(0.2 \mathrm{~kg} / \mathrm{s}\). The condensate leaves the tubes as a saturated liquid at \(40^{\circ} \mathrm{C}\). The rate of heat transfer to air is (a) \(34 \mathrm{~kJ} / \mathrm{s}\) (b) \(268 \mathrm{~kJ} / \mathrm{s}\) (c) \(453 \mathrm{~kJ} / \mathrm{s}\) (d) \(481 \mathrm{~kJ} / \mathrm{s}\) (e) \(515 \mathrm{~kJ} / \mathrm{s}\)

Short Answer

Expert verified
a) 402 kJ/s b) 450 kJ/s c) 470 kJ/s d) 481 kJ/s Answer: d) 481 kJ/s

Step by step solution

01

Determine the enthalpies

First, we need to find the enthalpies of the saturated water vapor and the saturated liquid at the given temperature. From the steam tables, we can look up these enthalpy values at 40°C: Enthalpy of saturated vapor, \(h_\text{v}\): \(2574.2\,\mathrm{kJ/kg}\) Enthalpy of saturated liquid, \(h_\text{l}\): \(167.57\,\mathrm{kJ/kg}\)
02

Calculate the enthalpy change

We will now calculate the change in enthalpy during the condensation process using the found enthalpies for the saturated vapor and the saturated liquid: Enthalpy change, \(\Delta h = h_\text{v} - h_\text{l}\) \(\Delta h = 2574.2\,\mathrm{kJ/kg} - 167.57\,\mathrm{kJ/kg} = 2406.63\,\mathrm{kJ/kg}\)
03

Calculate the rate of heat transfer

The rate of heat transfer is the product of the mass flow rate and the change in enthalpy: Rate of heat transfer, \(Q = \text{mass flow rate} \times \Delta h\) We are given the mass flow rate as 0.2 kg/s: \(Q = (0.2\,\mathrm{kg/s}) \times 2406.63\,\mathrm{kJ/kg} = 481.33\,\mathrm{kJ/s}\)
04

Find the answer in the given options

We need to compare our result to the given options to find which one is correct. Our calculated rate of heat transfer is: \(Q = 481.33\,\mathrm{kJ/s}\) Comparing this to the given options, we see that option (d) is the closest: (d) \(481\,\mathrm{kJ/s}\) Therefore, the correct answer is (d) \(481\,\mathrm{kJ/s}\).

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Most popular questions from this chapter

A shell-and-tube heat exchanger with 2-shell passes and 4-tube passes is used for cooling oil \(\left(c_{p}=2.0 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right)\) from \(125^{\circ} \mathrm{C}\) to \(55^{\circ} \mathrm{C}\). The coolant is water, which enters the shell side at \(25^{\circ} \mathrm{C}\) and leaves at \(46^{\circ} \mathrm{C}\). The overall heat transfer coefficient is \(900 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). For an oil flow rate of \(10 \mathrm{~kg} / \mathrm{s}\), calculate the cooling water flow rate and the heat transfer area.

Can the temperature of the hot fluid drop below the inlet temperature of the cold fluid at any location in a heat exchanger? Explain.

A cross-flow heat exchanger with both fluids unmixed has an overall heat transfer coefficient of \(200 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), and a heat transfer surface area of \(400 \mathrm{~m}^{2}\). The hot fluid has a heat capacity of \(40,000 \mathrm{~W} / \mathrm{K}\), while the cold fluid has a heat capacity of \(80,000 \mathrm{~W} / \mathrm{K}\). If the inlet temperatures of both hot and cold fluids are \(80^{\circ} \mathrm{C}\) and \(20^{\circ} \mathrm{C}\), respectively, determine the exit temperature of the cold fluid.

A shell-and-tube heat exchanger is to be designed to cool down the petroleum- based organic vapor available at a flow rate of \(5 \mathrm{~kg} / \mathrm{s}\) and at a saturation temperature of \(75^{\circ} \mathrm{C}\). The cold water \(\left(c_{p}=4187 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) used for its condensation is supplied at a rate of \(25 \mathrm{~kg} / \mathrm{s}\) and a temperature of \(15^{\circ} \mathrm{C}\). The cold water flows through copper tubes with an outside diameter of \(20 \mathrm{~mm}\), a thickness of \(2 \mathrm{~mm}\), and a length of \(5 \mathrm{~m}\). The overall heat transfer coefficient is assumed to be \(550 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and the latent heat of vaporization of the organic vapor may be taken to be \(580 \mathrm{~kJ} / \mathrm{kg}\). Assuming negligible thermal resistance due to pipe wall thickness, determine the number of tubes required.

Consider a water-to-water double-pipe heat exchanger whose flow arrangement is not known. The temperature measurements indicate that the cold water enters at \(20^{\circ} \mathrm{C}\) and leaves at \(50^{\circ} \mathrm{C}\), while the hot water enters at \(80^{\circ} \mathrm{C}\) and leaves at \(45^{\circ} \mathrm{C}\). Do you think this is a parallel-flow or counterflow heat exchanger? Explain.
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