Find Area Enclosed by Thermodynamic Cycle

In summary, the question involves finding the area enclosed by the shape ABCD, with equations for AB and CD provided. The method used involves finding the area of the rectangular shape (C-B)*9 and subtracting the integral of AB with specified limits. The final answer obtained was 67.7, rounded to 3 significant figures.
  • #1
jackscholar
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Homework Statement


The question is pretty much explained in the picture.
The area ABCD is enclosed, i need to find that area. The equation for AB is P=0.8+8.6e^(-0.3V) and the equation for CD is P=1.2+9.6e^-(0.1V)
What I did was find the area enclosed by the rectangular shape (C-B)*9. From there I subtracted the integral of the equation AB with the upper and lower limits 2.076 and 0.159 respectively. I then surmised that if I subtracted the integral of AB from (25 (upper) to 2.076 (lower)) from CD then it would give me the rest of the Area. I ended up getting 67.7 doing this. Is this correct?
 

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  • #2
jackscholar said:

Homework Statement


The question is pretty much explained in the picture.
The area ABCD is enclosed, i need to find that area. The equation for AB is P=0.8+8.6e^(-0.3V) and the equation for CD is P=1.2+9.6e^-(0.1V)
What I did was find the area enclosed by the rectangular shape (C-B)*9. From there I subtracted the integral of the equation AB with the upper and lower limits 2.076 and 0.159 respectively. I then surmised that if I subtracted the integral of AB from (25 (upper) to 2.076 (lower)) from CD then it would give me the rest of the Area. I ended up getting 67.7 doing this. Is this correct?

That answer is OK, rounded to 3 significant figures.
 

1. What is the purpose of finding the area enclosed by a thermodynamic cycle?

The area enclosed by a thermodynamic cycle represents the net work done by the system during one complete cycle. It is an important measure of the efficiency of the cycle and can also provide insights into the thermodynamic processes happening within the system.

2. How is the area enclosed by a thermodynamic cycle calculated?

The area can be calculated by plotting the pressure-volume (PV) curve of the system and finding the area under the curve using integration. Alternatively, the area can also be calculated using the work done and heat transfer values for each process within the cycle.

3. What are some common types of thermodynamic cycles?

Some commonly studied thermodynamic cycles include the Carnot cycle, Otto cycle, Rankine cycle, and Brayton cycle. These cycles are used in various engineering applications, such as power generation and refrigeration.

4. How does the area enclosed by a thermodynamic cycle relate to the efficiency of the cycle?

The larger the area enclosed by a thermodynamic cycle, the more work is being done by the system. This generally indicates a more efficient cycle, as it is able to convert more heat into work. However, the specific efficiency of a cycle also depends on other factors, such as the type of cycle and the properties of the working fluid.

5. What are some factors that can affect the area enclosed by a thermodynamic cycle?

The area enclosed by a thermodynamic cycle can be affected by various factors, such as the type of cycle, the working fluid used, the temperature and pressure conditions, and any losses or inefficiencies within the system. Changes in these factors can alter the shape and size of the PV curve, and therefore, the area enclosed by the cycle.

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