Steam is to be condensed in the condenser of a steam power...

Steam is to be condensed in the condenser of a steam power plant at a temperature of $50^{\circ} \mathrm{C}$ with cooling water from a nearby lake, which enters the tubes of the condenser at $18^{\circ} \mathrm{C}$ at a rate of $101 \mathrm{kg} / \mathrm{s}$ and leaves at $27^{\circ} \mathrm{C}$ Determine the rate of condensation of the steam in the condenser.

Key Concepts

Phase Change and Latent Heat

Phase change refers to the transformation of a substance from one state of matter to another, such as steam condensing into water. During condensation, the substance releases latent heat, which is the energy released or absorbed during a phase change at a constant temperature and pressure. This concept is crucial in understanding how the energy from condensing steam is transferred to another medium.

Energy Balance

The principle of energy balance states that energy is neither created nor destroyed, only transferred. In the context of a steam power plant, the heat released by condensing steam must equal the heat gained by the cooling water. Setting up an energy balance allows for the determination of unknown quantities, such as the rate of steam condensation, by equating the heat released during phase change to the sensible heat gained in the cooling water.

Specific Heat Capacity

Specific heat capacity is a property of a substance that indicates the amount of heat required to raise the temperature of a unit mass by one degree Celsius. In this problem, it is used to calculate the amount of heat absorbed by the cooling water as it heats up while passing through the condenser, allowing the energy transferred from the steam to be quantified.

Mass Flow Rate

Mass flow rate is the amount of mass passing through a given surface per unit time. In thermal systems, it is an essential parameter for calculating how much energy is transferred when a fluid undergoes a temperature change over time. Here, the mass flow rate of the cooling water is critical in determining the total heat absorbed as it heats from the inlet to the outlet temperature.

Transcript

00:01 So for this question, we need to set out the energy balance equation here, which is e .9 equal e.

00:05 And if we expand it, we have qdin plus mdah1 is equal mdah2.

00:09 Qdi here is the rate of a heat transfer to the cooling water.

00:15 And mdi here is the mass flow rate for the cooling water.

00:20 And the h1 here is the initial entropy for the cooling water.

00:30 And h2 here is the final entropy for the cooling water.

00:35 If we do some arrangement here, we have q -dion is equal to m -dha -t times h2 minus h1, which is equal to m -dhawn 10 -cp2 minus t1.

00:42 Cp is a specific heat and constant pressure for the water and t2 is the final temperature for the cooling water and t1 is the initial temperature for the cooling water.

00:51 And we also know that the rate of heat transfer into the cooling water can be equal to the rate of a condensation of the sting in the condenser multiplied by the heat of vaporization.

01:03 According to energy conservation law.

01:06 Because when the rate of heat transferred to the cooling water, that means that these things also losing the heat from itself, since it's transferring to the cooling water.

01:17 So now we can use...

01:21 Actually, this one should be condensation.

01:24 So m .d.

01:25 Condensation...

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