(a)
The temperature after the adiabatic expansion.
(a)
Answer to Problem 47P
The temperature after the adiabatic expansion is
Explanation of Solution
Given:
The initial pressure of gas is
The initial temperature is
The final temperature is
Formula used:
The temperature after the adiabatic expansion is given as,
Here,
The volume after adiabatic expansion is given as,
Here,
The final pressure is given as,
Calculation:
The volume occupied by the gas at
For the fixed amount of gas the pressure at adiabatic expansion is can be calculated as,
The final pressure is calculated as,
The volume after adiabatic expansion is calculated as,
The temperature after the adiabatic expansion is calculated as,
Conclusion:
Therefore, the temperature after the adiabatic expansion is
(b)
The heat absorbed or released by the system during each step.
(b)
Answer to Problem 47P
The heat energy absorbed during the process 1-2 is
Explanation of Solution
Formula used:
The heat energy during the constant volume process 1-2 is given as,
Here,
Here,
The heat energy during the constant pressure process 3-1 is given as,
Here,
Calculation:
The heat energy during the constant volume process 1-2 is calculated as,
The process 2-3 is an adiabatic process. The heat energy for the process 2-3 is calculated as,
The heat energy during the constant pressure process 3-1 is given as,
The negative sign shows that heat is released during the process.
Conclusion:
Therefore, the heat energy absorbed during the process 1-2 is
(c)
The efficiency of the cycle.
(c)
Answer to Problem 47P
The efficiency of the cycle is
Explanation of Solution
Formula used:
The efficiency of the cycle is given as,
Here,
The total work during the cycle is given as,
Calculation:
The total work during the cycle is calculated as,
The efficiency of the cycle is calculated as,
Further solving the above equation as,
Conclusion:
Therefore, the efficiency of the cycle is
(d)
The efficiency of a Carnot cycle operating between the extreme temperatures.
(d)
Answer to Problem 47P
The efficiency of a Carnot cycle operating between the extreme temperatures is
Explanation of Solution
Formula used:
The efficiency of the Carnot cycle at extreme temperature (
Calculation:
The efficiency of the Carnot cycle at extreme temperature (
Further solving the above equation as,
Conclusion:
Therefore, the efficiency of a Carnot cycle operating between the extreme temperatures is
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Chapter 19 Solutions
Physics for Scientists and Engineers, Vol. 3
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