Water is the working fluid in an ideal Rankine cycle with...

Water is the working fluid in an ideal Rankine cycle with reheat. Superheated vapor enters the turbine at $8 \mathrm{MPa}$, $440^{\circ} \mathrm{C}$, and the condenser pressure is $8 \mathrm{kPa}$. Steam expands through the first-stage turbine to $0.5 \mathrm{MPa}$ and then is reheated to $440^{\circ} \mathrm{C}$. Determine for the cycle (a) the rate of heat addition, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam entering the first-stage turbine. (b) the thermal efficiency. (c) the rate of heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per $\mathrm{kg}$ of steam entering the first-stage turbine.

Water is the working fluid in an ideal Rankine cycle with reheat. Superheated vapor enters the turbine at $8 \mathrm{MPa}$, $440^{\circ} \mathrm{C}$, and the condenser pressure is $8 \mathrm{kPa}$. Steam expands through the first-stage turbine to $0.5 \mathrm{MPa}$ and then is reheated to $440^{\circ} \mathrm{C}$. Determine for the cycle
(a) the rate of heat addition, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam entering the first-stage turbine.
(b) the thermal efficiency.
(c) the rate of heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per $\mathrm{kg}$ of steam entering the first-stage turbine.

Key Concepts

Steam Properties and Steam Tables

Steam properties such as pressure, temperature, and enthalpy are critical for the analysis of power cycles. Steam tables provide the necessary thermodynamic data to determine these properties at various states in the cycle. Accurate determination of steam properties using these tables is essential for calculating energy transfers, work outputs, and overall cycle performance.

Heat Addition Analysis

Heat addition analysis concerns calculating the energy input required to convert the working fluid from a compressed liquid into superheated vapor, and in the case of reheat cycles, the additional heat input required during the reheat phase. This involves understanding changes in enthalpy during phase changes and temperature increases, which is crucial for evaluating the energy balance of the cycle.

Energy Balance in Turbines

The energy balance in turbines involves the application of the first law of thermodynamics to determine the work output of the turbine during the expansion process. This requires accounting for the enthalpy changes of the steam as it expands, whether through a single-stage expansion or multiple stages with reheat, to calculate the net work produced in the cycle.

Reheat Process

The reheat process is a modification of the basic Rankine cycle where steam, after an initial expansion in a turbine, is reheated before further expansion. This process increases the average temperature at which heat is added, reducing moisture content in the later stages of turbine expansion, improving overall efficiency, and preventing damage to turbine blades from wet steam.

Thermal Efficiency

Thermal efficiency is a measure of a cycle's performance, defined as the ratio of the net work output to the heat energy input. In the context of power cycles like the Rankine cycle, it provides insight into how effectively the cycle converts the supplied thermal energy into useful mechanical work.

Rankine Cycle

The Rankine cycle is a thermodynamic process model that describes the generation of work from heat, typically in steam power plants. It involves the conversion of water into steam, expansion of the steam in a turbine to do work, condensation of the exhaust steam, and pumping it back to the boiler. Its analysis is essential for understanding how thermal energy is converted into mechanical work and then into electrical energy.

Transcript

00:01 Reduction of thermodynamics for this particular problem that has a reheat, the ranking cycle, wanted to determine the rate of heat transfer, okay? rate of addition to the working fluid flowing through the turbine, dusting, to the turbine, and as well as the thermal efficiency and the rate of heat transfer from the working through the condenser.

00:28 All right so if we have these okay this and this and the system is uh reheated at this uh pressure is at five bar because at this pressure back to uh 440 degree celsius something like this let's say this one let's make it uh okay something like attitude okay okay so that's let's put it that way okay and we have this so if this is at the reheat pressure 5thar all right and we have this is point 1 point 2 prime okay this temperature in degrees celsius 0 .3 i will call this point point 3 prime all right we call this place which is reached back to 4 and 40 degrees celsius 3 prime prime or having that double mark if you check from the table at this point you're going to have it to be equal to 440 degrees celsius a 5 bar is going to give us 5 this kilo kilo per kilogram all right all right kilo per kilogram so you can so this is at 440 looking to 440 again this entrance degrees celsius all right you will check this and we check this on page at three prime.

03:01 You're going to give you three to three to four six point one, four six point one, kilojou per kilogram and of course it's at four hundred and forty degrees celsius.

03:19 Okay, that is the temperature and the pressure is at 80 bar.

03:25 The pressure there is at 80 bar.

03:29 80 bar.

03:33 Why here the pressure is at 5 .5.

03:36 It's already indicated longer at 9 already.

03:39 Alright, so we can at 4, let's call this place 0 .4.

03:44 It's going to give when you check it, it's going to give you equal to 2577 kiloj -j -per kilogram.

03:55 All right, 2 prime.

03:58 At two let's call this place two prime okay if you give you when you check it zero point sorry 274 it's point seven kilo per kilogram so all the enterpes are in kilo jou per kilogram the entropy is in kilo per kilogram the entropys are in kilo per kilogram okay all right so that's what we're going to have so if we look at the rate of heat addition now okay he's going to give us a q, just call it that dot, in, is equal to q, is going to give us at 3 prime, minus 2, okay, plus after.

05:11 So these are subscripts with all those numbers at the bottom, and the plus that subsprits, okay? 3 prime, prime, okay? so if you do this one, this one, that was going to give you.

05:25 So the work now is going to give us a specific goal in there.

05:32 Okay, if you check it at point one, it's going to give you 1 .00, sorry, one point, yes, 1 .0084 and standards the power of minus three, okay, cubic meter per kilogram, right? so p2 minus p1, okay? so which is 80 by minus 0 .085.

05:58 So the pressure here, the compressor pressure is 0 .0 .0 bar, right? so if you plug in values there, you will arrive at your answer to be 0 .081 kilo per kilogram.

06:29 So we can just get our h at 1 .2.

06:33 Just give you your 0 .0 .801...

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