2nd Law of Thermodynamics

In summary, an electric generating station with an electric output power of 1.20 MW and a turbine with two-thirds the efficiency of a Carnot engine exhausts energy by heat at a rate of 2/3(1-371/Th) as a function of the fuel combustion temperature Th. The exhaust power for Th = 838°C would be 1.20 MW, and the value of Th for which the exhaust power would be only half as large is 774.5°C.
  • #1
physics_geek
84
0

Homework Statement


An electric generating station is designed to have an electric output power 1.20 MW using a turbine with two-thirds the efficiency of a Carnot engine. The exhaust energy is transferred by heat into a cooling tower at 98°C.

(a) Find the rate at which the station exhausts energy by heat, as a function of the fuel combustion temperature Th.

(b) Find the exhaust power for Th = 838°C.


(c) Find the value of Th for which the exhaust power would be only half as large as in part (b).




Homework Equations


P=W/t e= 1- tc/th


The Attempt at a Solution


ok i really don't know where to start on this one
any kind of help would be appreciated..thanks!
 
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  • #2
physics_geek said:

Homework Statement


An electric generating station is designed to have an electric output power 1.20 MW using a turbine with two-thirds the efficiency of a Carnot engine. The exhaust energy is transferred by heat into a cooling tower at 98°C.

(a) Find the rate at which the station exhausts energy by heat, as a function of the fuel combustion temperature Th.

(b) Find the exhaust power for Th = 838°C.


(c) Find the value of Th for which the exhaust power would be only half as large as in part (b).
First of all, you have to determine how much heat per unit of time the station has to exhaust. If the efficiency if 2/3 of a Carnot engine operating between Th and 98C what is the efficiency? (be careful to convert temps to K).

How much heat is needed to produce 1.2 MW? So how much heat is left over after you subtract the 1.2 MW output?

AM
 
  • #3
so does that mean the efficiency would be
e = 2/3(1- 371/Th) ??

what do i do with this..it asks for the rate at which it exhausts energy by heat
 
  • #4
Trying to figure this part out aswell. Any additional direction would be appreciated.
 
  • #5
physics_geek said:
so does that mean the efficiency would be
e = 2/3(1- 371/Th) ??
That looks right.
what do i do with this..it asks for the rate at which it exhausts energy by heat
You are trying to found Qout.
Use the definition of efficiency (ie in terms of Work done to Qin) to give you Qin. How is the work done related to Qin and Qout?

AM
 
  • #6
ok yea i don't understand this at all

so if 2/3(1-371/Th) is right..wat am i solving for..that just gives me the efficiency
im so confused!
 
  • #7
Thanks Andrew, that helped me.

physics_geek said:
ok yea i don't understand this at all

so if 2/3(1-371/Th) is right..wat am i solving for..that just gives me the efficiency
im so confused!

You're solving for Q_out, which is like the energy you put in minus the work that you put out. I was solving for Q_in so that part confused me.

However, if you can get Q_in then getting Q_out is just one step away.

Use the definition of efficiency (ie in terms of Work done to Qin) to give you Qin. How is the work done related to Qin and Qout?

If you can do this then the problem is solved. You have the right efficiency, but that efficiency can also equal something in terms of work and Q_in <--- useful.
 

1. What is the 2nd Law of Thermodynamics?

The 2nd Law of Thermodynamics is a fundamental principle in physics that states that the total entropy (or disorder) of a closed system will always increase over time. This means that energy will naturally spread out and become less concentrated, resulting in less available energy for work.

2. How does the 2nd Law of Thermodynamics relate to energy?

The 2nd Law of Thermodynamics is closely related to energy because it dictates how energy behaves in a closed system. It states that energy will always flow from areas of high concentration to areas of low concentration, resulting in a decrease in usable energy over time.

3. Can the 2nd Law of Thermodynamics be violated?

No, the 2nd Law of Thermodynamics is considered a universal law and cannot be violated. It has been tested and observed in various systems and has always been found to hold true.

4. How does the 2nd Law of Thermodynamics affect living organisms?

The 2nd Law of Thermodynamics applies to all systems, including living organisms. It means that living organisms must constantly take in energy and convert it into usable forms in order to maintain their organization and complexity. This process of converting energy is known as metabolism.

5. Can the 2nd Law of Thermodynamics be applied to everyday life?

Yes, the 2nd Law of Thermodynamics can be seen in many aspects of everyday life. For example, a cup of hot coffee will eventually cool down as energy spreads out and becomes less concentrated. Additionally, the aging process of living organisms can also be attributed to the 2nd Law of Thermodynamics as their energy becomes less concentrated and less available for maintaining their complex structures.

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