Interpretation:
The expressions to calculate the work and heat for the four steps of a Carnot cycle are to be stated. The
Concept introduction:
The Carnot cycle represents the relationship between the efficiency of a steam engine and the temperatures. It was given by Carnot who stated that every engine gets the heat from a high-temperature reservoir. Some of the heat is converted to the work during the process. The Carnot cycle has four major steps:
Step 1: Reversible isothermal expansion
Step 2: Reversible adiabatic expansion
Step 3: Reversible isothermal compression
Step 4: Reversible adiabatic compression
Answer to Problem 3.65E
The expressions to calculate the work and heat for the four steps of a Carnot cycle are given below.
The
The total work and heat of the cycle is
The value of
Explanation of Solution
For the Carnot cycle, the first and the third step are reversible isothermal processes.
On the other hand, the second and the fourth step are reversible adiabatic processes. So, the expressions to calculate the heat for four steps can be written as shown below.
The variables
From the first law of
The work done for reversible adiabatic processes is given by the formula given below.
Therefore, the expressions to calculate the work for second and the fourth steps can be written as shown below.
Assume
Total heat can be calculated as shown below.
Substitute the values in the above equation as shown below.
Work done for the first and third step can be calculated as shown below.
Substitute the values in the above equation as shown below.
Work done for the second and fourth step can be calculated as shown below.
Substitute the values in the above equation as shown below.
The work of the cycle is calculated by using the formula given below.
Substitute the values in the above equation as shown below.
The entropy change is calculated by the formula given below.
The steps first and the third are reversible isothermal processes; so, the temperature is constant, and at a constant temperature, the heat change is constant. The values of changes in the energy, that is,
The expressions to calculate the work and heat for the four steps of a Carnot cycle are given below.
The
The total work and heat of the cycle is
The value of
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Chapter 3 Solutions
Physical Chemistry
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