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The second law of thermodynamics: The heat flow statement : Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the reverse direction.
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The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Dec 29, 2015

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Pierce Blair
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Page 1: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the reverse direction.

Page 2: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

A heat engine is a device that uses heat to perform work. The efficiency e of a heat engine is the ratio of work W done to the input heat QH. Efficiency is often stated as a percentage.

Page 3: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

For a heat engine the total of the work W done and the rejected heat QC must equal the input heat QH.

QH = W + QC

Page 4: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Ex 6 - An automobile has an efficiency of 22.0% and produces 2510 J of work. How much heat is rejected by the engine?

Page 5: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

A reversible process is one in which both the system (the gas) and its environment (the piston and the rest of the universe) can be returned to exactly the states they were in before the process occurred. A process that involves an energy-dissipating mechanism cannot be reversible.

Page 6: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Sadi Carnot proposed that a heat engine has maximum efficiency when the processes within the engine are reversible.

Page 7: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Carnot’s Principle: No irreversible engine operating between two reservoirs at constant temperatures can have a greater efficiency than a reversible engine operating between the same temperatures. Furthermore, all reversible engines operating between the same temperatures have the same efficiency.

Page 8: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Notice that this law does not state that a reversible engine is 100% efficient. Carnot’s law is an alternative statement of the second law of thermodynamics.

Page 9: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

A Carnot engine is an idealized reversible engine.

The Kelvin scale is based on the comparative temperatures of the reservoirs of a Carnot engine.

Page 10: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

The ratio of rejected heat QC to input heat QH is:

QC/ QH = TC / TH.

TC and TH must be expressed in Kelvins.

Page 11: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

The efficiency of a Carnot engine is equal to 1 - TC/TH.

Page 12: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Ex 7 - A heat engine has a hot reservoir at 298.2 K and a cold reservoir at 280.2 K. (a) Find the maximum possible efficiency for such an engine. (b) Determine the minimum input heat QH that would be needed if a number of these heat engines were to produce an amount of work equal to the 9.3 x 1019 J of energy that the US consumed in 1994.

Page 13: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

The efficiency is low because the temperatures are so close to being the same. The efficiency increases as TC approaches absolute zero. Experiments have shown that it is not possible to cool a substance to 0 K; therefore a 100% efficient heat engine is not possible.

Page 14: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Refrigerators, air conditioners, and heat pumps use work to force heat to flow from the cold reservoir to the hot reservoir; this is called a refrigeration process.

QH = W + QC

Page 15: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

If the refrigeration system is an ideal device, then QC/QH = TC/TH applies, just as for a Carnot engine.

Page 16: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

QH = W + QC and QC/QH = TC/TH are the two equations used for Carnot refrigeration systems.

Page 17: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Ex 8 - An ideal or Carnot heat pump is used to heat a house to a temperature of TH = 294 K. How much work must be done by the pump to deliver QH = 3350 J of heat into the house when the outdoor temperature TC is (a) 273 K and (b) 252 K?

Page 18: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Irreversible processes cause a machine to lose some of its ability to perform work. This partial loss is expressed in terms of entropy. Heat divided by temperature is the change in entropy for a reversible system:∆S = (Q/T)R. The subscript R means “reversible” system.

Page 19: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Reversible processes do not alter the total entropy of the universe. ∆Suniverse = 0 for a reversible process.

Page 20: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Ex 11 - 1200 J of heat flows spontaneously through a copper rod from a hot reservoir at 650 K to a cold reservoir at 350 K. Determine the amount by which this irreversible process changes the entropy of the universe, assuming that no other changes occur.

Page 21: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Any irreversible process increases the entropy of the universe. ∆Suniverse > 0 for an irreversible process.The entropy of the universe continually increases.

Page 22: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

The second law of thermodynamics stated in terms of entropy - The total entropy of the universe does not change when a reversible process occurs (∆Suniverse = 0) and increases when an irreversible process occurs (∆Suniverse > 0).

Page 23: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Ex 12 - Suppose 1200 J of heat is used as input for a n engine under two different conditions. In the first, the heat is supplied by a hot reservoir whose temperature is 650 K. In the other, the heat flows irreversibly through a copper rod into a second reservoir whose temperature is 350 K and then enters the engine. In either case, a 150-K reservoir is used as the cold reservoir. For each case, determine the maximum amount of work that can be obtained from the 1200 J of heat.

Page 24: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

The previous problem showed that 240 J less work could be performed by the system with a lower temperature difference. Example 11 showed that the entropy of the universe increased by 1.6 J/K.

Page 25: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

Wunavailable = T0∆Suniverse

In the previous cases, Wunavailable = 240 J, T0 = the cold reservoir temp of 150 K, ∆Suniverse = 1.6 J/K; so: Wunavailable = 150 K • 1.6 J/K = 240 J.

Page 26: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

An increase in entropy is associated with an increase in disorder.

Page 27: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.

The third law of thermodynamics - It is not possible to lower the temperature of any system to absolute zero in a finite number of steps.

Page 28: The second law of thermodynamics: The heat flow statement: Heat flows spontaneously from a substance at a higher temperature to a substance at a lower.