Second law of thermodynamic question

This means that the heat transfer to the surroundings is higher than the maximum possible power, resulting in a lower temperature of the exiting steam.
  • #1
sean/mac
8
0
A steam turbine in a power plant accepts 4500 kg/hr of steam at 60 bar and 500°C and exhausts steam at 10 bar. Heat transfer to the surroundings (Tsurr = 300K) at a rate of 70 kW.

(a) What condition needs to be satisfied for the turbine to generate the maximum possible power? (2 marks)

(b) Calculate the specific entropy of the steam leaving the turbine when the latter is generating the maximum possible power. (8 marks)

(c) Show that at this condition, the exiting steam temperature is 199.9°C. (3 marks)

(d) Calculate the maximum possible power generated by the turbine. (5 marks)

(e) Calculate the actual power of the turbine when the isentropic efficiency is 66.5%. (3 marks)

(f) Without doing any calculation, do you expect the actual temperature of the exiting steam be higher or lower than 199.9°C? Briefly explain your decision. (4 marks)


I think once i know (b) i can complete the rest

For (a) i think the system process has to be reversible??

For (b) i thought the steady state equation is 0=m(s2-s1)-Qrev/T
but where is work in this equation??

any help is appreciated
 
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  • #2
!(a) For the turbine to generate the maximum possible power, the process must be reversible. (b) The specific entropy of the steam leaving the turbine when generating the maximum possible power can be calculated using the steady-state energy equation: 0 = m(s2-s1) - Qrev/T, where m is the mass flow rate of the steam, s1 and s2 are the specific entropies at the inlet and outlet of the turbine respectively, Qrev is the heat transfer to the surroundings, and T is the temperature at the inlet of the turbine. (c) The exiting steam temperature can be determined by using the first law of thermodynamics, which states that energy is conserved. Therefore, the energy entering the turbine (m x cv x (T2 - T1)) must be equal to the energy leaving the turbine (m x cv x (T3 - T2) + Qrev). Rearranging this equation gives T3 = (T2 x m x cv + Qrev) / (m x cv), and substituting the given values gives T3 = 199.9°C. (d) The maximum possible power generated by the turbine can be calculated using the first law of thermodynamics, which states that energy is conserved. Therefore, the energy entering the turbine (m x cv x (T2 - T1)) must be equal to the energy leaving the turbine (m x cv x (T3 - T2) + Qrev). Rearranging this equation gives Pmax = m x cv x (T2 - T1) - Qrev/t, where t is the time. Substituting the given values gives Pmax = 70 kW. (e) The actual power of the turbine when the isentropic efficiency is 66.5% can be calculated using the steady-state energy equation: Pact = Pmax x n, where n is the isentropic efficiency. Substituting the given values gives Pact = 70 kW x 0.665 = 46.55 kW. (f) I expect the actual temperature of the exiting steam to be lower than 199.9°C because the actual power (46.55 kW) is lower than the maximum possible power (70 kW).
 

Related to Second law of thermodynamic question

What is the second law of thermodynamics?

The second law of thermodynamics is a fundamental principle in physics that states that the total entropy of a closed system will always increase over time. This means that energy will always tend to spread out and become more disordered.

What is entropy?

Entropy is a measure of the disorder or randomness in a system. The second law of thermodynamics states that the total entropy of a closed system will always increase, meaning that the system will tend towards a more disordered state over time.

How does the second law of thermodynamics relate to heat and energy?

The second law of thermodynamics is closely related to the concept of heat and energy. It explains that energy will always tend to disperse and become less concentrated over time, and that heat will naturally flow from hotter to colder objects.

Why is the second law of thermodynamics important?

The second law of thermodynamics is important because it is a fundamental principle that helps us understand the behavior of energy and matter in the universe. It also has practical applications in fields such as engineering and chemistry.

Are there any exceptions to the second law of thermodynamics?

While there are some systems that may appear to violate the second law of thermodynamics, such as living organisms that can create order and complexity, these systems still follow the overall trend of increasing entropy. Additionally, the second law of thermodynamics is a statistical law, meaning that there is a small probability of random fluctuations resulting in a decrease in entropy, but these occurrences are extremely rare.

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