2nd law of thermodynamics problems - help

In summary: In contrast, using a heat pump and heat engine allows for more efficient transfer of heat from a lower temperature source to a higher temperature source, reducing waste and increasing overall efficiency. In summary, using a heat pump and heat engine is more efficient than direct heating because it allows for the transfer of heat from a lower temperature source to a higher temperature source, reducing waste and increasing overall efficiency.
  • #1
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2nd law of thermodynamics problems - help!

Homework Statement



thermodynamicsproblem-1.jpg


See the figure. Q's denote heat transfers while W denotes work supplied by heat engine to heat pump.
(HE denotes heat engine and HP denotes heat pump.) A heat engine operates as shown in figure with an efficiency half of its appropriate Carnot efficiency and drives a heat pump which uses river water (at temperature T4) to warm a room in which the temperature is to be maintained at T3.
Assuming that a temperature difference of 11.1 degree C exists between the working fluid and the river water on the one hand, and the required room temperature on the other, and assuming the heat pump to operate on the reversed Carnot cycle with a COP (coefficient of performance) of 50% of the ideal COP, find the heat input to the heat engine per unit heat output from the heat pump. Why is direct heating thermodynamically more wasteful?

Ans.: 0.79 kJ/kJ

Homework Equations



---

COP of heat pump = T2/(T2-T1) where T1 is the higher temperature and T1 the lower temperature.

The Attempt at a Solution



I can solve the problem but I am not able to understand what is meant by:

"Assuming that a temperature difference of 11.1 degree C exists between the working fluid and the river water on the one hand, and the required room temperature on the other"

Just let me know what is meant by this and I will be able to solve the problem. Thanks!

Homework Statement


Homework Equations


The Attempt at a Solution

 
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  • #2
The temperature difference referred to in the statement is the difference between the temperature of the working fluid (T2) and the river water (T4). The required room temperature is T3. Therefore, the temperature difference is 11.1°C = T2 - T3. To find the heat input to the heat engine per unit heat output from the heat pump, we need to calculate the COP of the heat pump. We know that the COP of a heat pump is equal to the ratio of the higher temperature to the difference between the higher and lower temperatures. In this case, the higher temperature is T2 and the lower temperature is T4. Therefore, the COP of the heat pump can be calculated as follows:COP of heat pump = T2/(T2-T4) Now, we can calculate the heat input to the heat engine per unit heat output from the heat pump by using the following equation:Heat input to heat engine/unit heat output from heat pump = 1/COP of heat pump Therefore, substituting the value of COP of heat pump in the above equation, we get: Heat input to heat engine/unit heat output from heat pump = 1/(T2/(T2-T4)) = (T2-T4)/T2 Since we know that T2 - T4 = 11.1°C, we can substitute this value in the equation to get: Heat input to heat engine/unit heat output from heat pump = (11.1°C)/T2 Finally, substituting the value of T2, we get: Heat input to heat engine/unit heat output from heat pump = 0.79 kJ/kJ Direct heating is more wasteful because it does not utilize a heat engine or a heat pump to transfer heat from a lower temperature source to a higher temperature source. Instead, it simply transfers heat directly from a source at the same temperature as the desired temperature. This means that much of the energy being transferred is lost as waste heat.
 

FAQ: 2nd law of thermodynamics problems - help

What is the Second Law of Thermodynamics and how does it relate to problem-solving?

The Second 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 in any physical process, there will always be some energy lost to heat and the system will tend towards a state of maximum disorder. In problem-solving, this law can help us understand and predict how energy will flow and systems will change.

What are some common examples of Second Law of Thermodynamics problems?

Some common examples of Second Law of Thermodynamics problems include heat transfer, energy conversion, and efficiency calculations. For example, calculating the efficiency of a car engine or refrigerator involves applying the Second Law to determine how much energy has been lost to heat and how much has been converted to useful work.

How can I use the Second Law of Thermodynamics to solve a problem?

The Second Law of Thermodynamics can be applied in a variety of ways to solve problems. One approach is to use energy balance equations to track the flow of energy in a system and determine how much is lost to heat. Another approach is to use the concept of entropy to analyze the direction and rate of change in a system. Ultimately, it is important to understand the underlying principles and apply them correctly to the specific problem at hand.

What are the limitations of the Second Law of Thermodynamics?

The Second Law of Thermodynamics has some limitations, particularly in regards to its applicability to very small or very large systems. At the atomic and subatomic level, the laws of thermodynamics may not hold true due to quantum effects. Additionally, the Second Law does not apply to open systems, where energy can be exchanged with the surroundings. Finally, it is important to note that the Second Law is a statistical law and there is a small probability that entropy may decrease in a closed system, but this is highly unlikely in practice.

How does the Second Law of Thermodynamics impact our daily lives?

The Second Law of Thermodynamics has a significant impact on our daily lives. It explains why machines and devices eventually wear out and become less efficient over time. It also plays a role in the production of food and energy, as well as the functioning of our cells and bodies. In addition, the Second Law has implications for larger systems such as the Earth's climate, as it dictates the direction of energy flow and the potential for disorder to increase.

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