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Chapter 1: Problem 150

Water enters a pipe at \(20^{\circ} \mathrm{C}\) at a rate of \(0.50 \mathrm{~kg} / \mathrm{s}\) and is heated to \(60^{\circ} \mathrm{C}\). The rate of heat transfer to the water is (a) \(20 \mathrm{~kW}\) (b) \(42 \mathrm{~kW}\) (c) \(84 \mathrm{~kW}\) (d) \(126 \mathrm{~kW}\) (e) \(334 \mathrm{~kW}\)

Short Answer

Expert verified
Answer: The rate of heat transfer to the water is \(84 \mathrm{~kW}\).

Step by step solution

01

Identify relevant information and equations

We are given the initial temperature (Ti) of water as \(20^{\circ} \mathrm{C}\), the final temperature (Tf) as \(60^{\circ} \mathrm{C}\), the mass flow rate (m) as \(0.50 \mathrm{~kg}/\mathrm{s}\), and the specific heat capacity (c) of water as \(4200 \mathrm{~J}/(\mathrm{kg}\cdot\mathrm{K})\). The rate of heat transfer (Q) can be calculated using the following equation: \(Q = cm(Tf - Ti)\) Where Q is the rate of heat transfer, c is the specific heat capacity, m is the mass flow rate, Tf and Ti are the final and initial temperatures, respectively.
02

Calculate the temperature difference

Calculate the difference between the final and initial temperature, which is the change in temperature: \(\Delta T = Tf - Ti = 60^{\circ} \mathrm{C} - 20^{\circ} \mathrm{C} = 40^{\circ} \mathrm{C}\)
03

Calculate the rate of heat transfer

Now, substitute the given values into the equation and calculate the rate of heat transfer: \(Q = (4200 \mathrm{~J}/(\mathrm{kg}\cdot\mathrm{K})) \times (0.50 \mathrm{~kg}/\mathrm{s}) \times 40\mathrm{K}\) \(Q = 84000 \mathrm{~J}/\mathrm{s} = 84 \mathrm{~kW}\) Thus, the rate of heat transfer to the water is option (c) \(84 \mathrm{~kW}\).

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Most popular questions from this chapter

Hot air at \(80^{\circ} \mathrm{C}\) is blown over a 2-m \(\times 4\) - \(\mathrm{m}\) flat surface at \(30^{\circ} \mathrm{C}\). If the average convection heat transfer coefficient is \(55 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), determine the rate of heat transfer from the air to the plate, in \(\mathrm{kW}\).

Engine valves \(\left(c_{p}=440 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right.\) and \(\left.\rho=7840 \mathrm{~kg} / \mathrm{m}^{3}\right)\) are to be heated from \(40^{\circ} \mathrm{C}\) to \(800^{\circ} \mathrm{C}\) in \(5 \mathrm{~min}\) in the heat treatment section of a valve manufacturing facility. The valves have a cylindrical stem with a diameter of \(8 \mathrm{~mm}\) and a length of \(10 \mathrm{~cm}\). The valve head and the stem may be assumed to be of equal surface area, with a total mass of \(0.0788 \mathrm{~kg}\). For a single valve, determine ( \(a\) ) the amount of heat transfer, \((b)\) the average rate of heat transfer, \((c)\) the average heat flux, and \((d)\) the number of valves that can be heat treated per day if the heating section can hold 25 valves and it is used 10 h per day.

Consider a flat-plate solar collector placed on the roof of a house. The temperatures at the inner and outer surfaces of the glass cover are measured to be \(33^{\circ} \mathrm{C}\) and \(31^{\circ} \mathrm{C}\), respectively. The glass cover has a surface area of \(2.5 \mathrm{~m}^{2}\), a thickness of \(0.6 \mathrm{~cm}\), and a thermal conductivity of \(0.7 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Heat is lost from the outer surface of the cover by convection and radiation with a convection heat transfer coefficient of \(10 \mathrm{~W} /\) \(\mathrm{m}^{2} \cdot \mathrm{K}\) and an ambient temperature of \(15^{\circ} \mathrm{C}\). Determine the fraction of heat lost from the glass cover by radiation.

In a power plant, pipes transporting superheated vapor are very common. Superheated vapor is flowing at a rate of \(0.3 \mathrm{~kg} / \mathrm{s}\) inside a pipe with \(5 \mathrm{~cm}\) in diameter and \(10 \mathrm{~m}\) in length. The pipe is located in a power plant at \(20^{\circ} \mathrm{C}\), and has a uniform pipe surface temperature of \(100^{\circ} \mathrm{C}\). If the temperature drop between the inlet and exit of the pipe is \(30^{\circ} \mathrm{C}\), and the specific heat of the vapor is \(2190 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\), determine the heat transfer coefficient as a result of convection between the pipe surface and the surrounding.

Using the parametric table and plot features of \(\mathrm{EES}\), determine the squares of the number from 1 to 100 in increments of 10 in tabular form, and plot the results.
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