Thermal Physics - Efficiency

[Peter G.]

Hello,

An electrical power station situated in Northern Canada uses water to cool the steam as it leaves the turbine. Suggest why the efficiency of the turbine would be greater in winter than in summer:

I first started to think in terms of the efficiency equation I have for heat engines:

1 - T_c/T_h but a decrease in the temperature of the cold sink would decrease the efficiency so I am a bit lost.

Could anyone please give me a hint so I can try and solve this?

Thanks,
Peter G.

 

[mrmiller1]

Hi Peter,
It is true that all power plants generally run better in the winter than in the summer. I've experienced this myself working at a nuclear power plant.
You're on the right track but it looks like you just misinterpreted the Carnot equation. When Tc decreases then the Carnot efficiency increases.

-For example,
T_c = 100K, T_h = 500K, η = 80%
T_c = 10K, T_h = 500K, η = 98%

-Remember that this is not the actual efficiency. It is only the maximum efficiency that can ever be achieved in an actual event.

-As a side note, the driving force for heat transfer is a temperature gradient. So when the temperature difference is greater there is a greater driving force for heat transfer to occur. In the turbine of a power plant the heat sink is much greater in the winter, therefore, heat is lost to its surroundings much faster.

 

[Peter G.]

Wow, thanks a lot for the comprehensive and thorough answer. You're great!

 

[Kratos321]

In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance in the high temperature state. The working substance generates work in the "working body" of the engine while transferring heat to the colder "sink" until it reaches a low temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid.
In general an engine converts energy to mechanical work. Heat engines distinguish themselves from other types of engines by the fact that their efficiency is fundamentally limited by Carnot's theorem. Although this efficiency limitation can be a drawback, an advantage of heat engines is that most forms of energy can be easily converted to heat by processes like exothermic reactions (such as combustion), absorption of light or energetic particles, friction, dissipation and resistance. Since the heat source that supplies thermal energy to the engine can thus be powered by virtually any kind of energy, heat engines are very versatile and have a wide range of applicability.
Heat engines are often confused with the cycles they attempt to mimic. Typically when describing the physical device the term 'engine' is used. When describing the model the term 'cycle' is used.

 

[rwisz]

Hello Peter,

The efficiency of a heat engine is affected by the temperature difference between the hot and cold reservoirs. In this case, the hot reservoir is the steam leaving the turbine and the cold reservoir is the water used for cooling. In winter, the temperature of the cold reservoir would be lower than in summer due to the colder climate. This lower temperature difference between the hot and cold reservoirs would result in a higher efficiency for the turbine. This is because a smaller temperature difference means less energy is lost to the surroundings, allowing more of the energy to be converted into useful work.