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Chapter 10: Problem 128

Saturated water vapor at \(40^{\circ} \mathrm{C}\) is to be condensed as it flows through a tube at a rate of \(0.2 \mathrm{~kg} / \mathrm{s}\). The condensate leaves the tube as a saturated liquid at \(40^{\circ} \mathrm{C}\). The rate of heat transfer from the tube 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
Answer: The rate of heat transfer is approximately \(477.2~\mathrm{kJ/s}\), which is closest to option (d) \(481 \mathrm{~kJ} / \mathrm{s}\) among the given choices.

Step by step solution

01

Identify the known variables

We know the mass flow rate \(\dot{m} = 0.2~\mathrm{kg/s}\) and the temperature \(T=40^{\circ}\mathrm{C}\)
02

Look up the enthalpy values of saturated liquid and vapor at \(40^{\circ} \mathrm{C}\)

Using a steam table, we find the values of enthalpy of saturated liquid (\(h_{f}\)) and saturated vapor (\(h_{g}\)) at \(40^{\circ} \mathrm{C}\): \(h_{f}=167.52~\mathrm{kJ/kg}\) \(h_{g}=2553.6~\mathrm{kJ/kg}\)
03

Calculate the enthalpy difference

The enthalpy difference can be found by subtracting the enthalpy of saturated liquid from saturated vapor: \(\Delta h = h_{g} - h_{f}\) \(\Delta h = 2553.6~\mathrm{kJ/kg} - 167.52~\mathrm{kJ/kg} = 2386.08~\mathrm{kJ/kg}\)
04

Calculate the rate of heat transfer

To calculate the rate of heat transfer, we multiply the mass flow rate with the enthalpy difference: \(\dot{Q} = \dot{m} \times \Delta h\) \(\dot{Q} = 0.2~\mathrm{kg/s} \times 2386.08~\mathrm{kJ/kg} = 477.216~\mathrm{kJ/s}\) The calculated rate of heat transfer is approximately \(477.2~\mathrm{kJ/s}\). Looking at the given options, option (d) is closest to our calculated value. So, the correct answer is (d) \(481 \mathrm{~kJ} / \mathrm{s}\).

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Most popular questions from this chapter

A 1-mm-diameter nickel wire with electrical resistance of \(0.129 \mathrm{\Omega} / \mathrm{m}\) is submerged horizontally in water at atmospheric pressure. Determine the electrical current at which the wire would be in danger of burnout in nucleate boiling.

A non-boiling two-phase flow of air and engine oil in a 25 -mm diameter tube has a bulk mean temperature of \(140^{\circ} \mathrm{C}\). If the flow quality is \(2.1 \times 10^{-3}\) and the mass flow rate of the engine oil is \(0.9 \mathrm{~kg} / \mathrm{s}\), determine the mass flow rate of air and the superficial velocities of air and engine oil.

An air conditioner condenser in an automobile consists of \(2 \mathrm{~m}^{2}\) of tubular heat exchange area whose surface temperature is \(30^{\circ} \mathrm{C}\). Saturated refrigerant-134a vapor at \(50^{\circ} \mathrm{C}\) \(\left(h_{f g}=152 \mathrm{~kJ} / \mathrm{kg}\right)\) condenses on these tubes. What heat transfer coefficent must exist between the tube surface and condensing vapor to produce \(1.5 \mathrm{~kg} / \mathrm{min}\) of condensate? (a) \(95 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (b) \(640 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (c) \(727 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (d) \(799 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) (e) \(960 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\)

When boiling a saturated liquid, one must be careful while increasing the heat flux to avoid burnout. Burnout occurs when the boiling transitions from boiling. (a) convection to nucleate (b) convection to film (c) film to nucleate (d) nucleate to film (e) none of them

Water is boiled at \(90^{\circ} \mathrm{C}\) by a horizontal brass heating element of diameter \(7 \mathrm{~mm}\). Determine the maximum heat flux that can be attained in the nucleate boiling regime.
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