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Questions and Answers
What is the actual work done during mechanically reversible, adiabatic compression when the process has an efficiency of 80%?
What is the change in heat (Q) during the mechanically reversible cooling process with an irreversible efficiency of 80%?
How does the work done in an irreversible process compare to the reversible process for mechanically reversible cooling?
What is the value of Q for the entire cycle considering the calculated changes in the processes mentioned?
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When performing adiabatic processes, work ( W) must be considered. What was the total work done in the process?
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What is the relationship between internal energy change, work, and heat in these thermodynamic processes?
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In the case of mechanically reversible processes, how is work (W) affected if the efficiency is less than 100%?
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What is the formula used to calculate the work done for the irreversible cooling process detailed in the content?
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What is the final temperature after the adiabatic compression when the volume changes to 0.008263 m³?
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In the given adiabatic process, the work done during compression is measured as what value?
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For the constant-volume step in the process, what is the heat transfer value?
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What is the relationship between Q and W for the process described?
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What is the heat capacity used in the calculations for the ideal gas?
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In the ideal gas compression process, the specific heat capacity is represented by which notation?
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During which process is no work done according to the provided information?
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What does the ideal gas equation suggest about the work done in reversible processes?
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What is the approximate value of γ for diatomic gases?
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In thermodynamics, how is the work for an irreversible process primarily calculated?
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Which of the following statements is true regarding property changes in reversible and irreversible processes?
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How does the work of an irreversible process compare to that of a reversible process if it produces work?
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What is the relationship between equations for property changes and the type of process (reversible or irreversible)?
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When calculating work for a process that requires work, how does the reversible process value compare to the actual irreversible process?
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What is the approximate γ value for simple polyatomic gases such as CO2 and NH3?
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What common characteristic do the equations for dUig, dHig, ΔUig, and ΔHig share?
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Study Notes
Work and Heat in Irreversible Processes
- For mechanically reversible, adiabatic compression, work ( W_{rev} = 998 , \text{J} ); with 80% efficiency, actual work ( W = \frac{998}{0.80} = 1248 , \text{J} ).
- First law of thermodynamics gives ( Q = \Delta U_{ig} - W = 998 - 1248 = -250 , \text{J} ).
Cooling Process
- Mechanically reversible cooling process requires work ( W_{rev} = 665 , \text{J} ); actual work ( W = \frac{665}{0.80} = 831 , \text{J} ).
- Change in internal energy ( \Delta U_{ig} = -998 , \text{J} ) leads to heat transfer ( Q = -998 - 831 = -1829 , \text{J} ).
System Work
- In a process where work is done by the system, irreversible work in absolute value is less than ( -1495 , \text{J} ).
- Actual work done ( W = 0.80 \times (-1495) = -1196 , \text{J} ).
- Since the internal energy change is zero in this step, heat transfer is ( Q = \Delta U_{ig} - W = 0 + 1196 = 1196 , \text{J} ).
Overall Cycle Summary
- Total change for the entire cycle shows ( \Delta U_{ig} ) and ( \Delta H_{ig} = 0 ).
- Cumulative heat transfer is ( Q = -250 - 1829 + 1196 = -883 , \text{J} ).
- Total work done in the cycle ( W = 1248 + 831 - 1196 = 883 , \text{J} ).
Characteristics of Real Gases
- Equations derived for mechanically reversible processes apply similarly to irreversible processes for ideal gases.
- Property changes ( dU_{ig}, dH_{ig}, \Delta U_{ig}, \Delta H_{ig} ) depend solely on the states' initial and final conditions.
Calculating Irreversible Work
- Work for irreversible processes is usually calculated in two steps:
- First, determine ( W ) for a reversible process accomplishing the same state change.
- Multiply or divide this value by efficiency to obtain actual work.
- If the process produces work, actual irreversible ( W ) is greater than reversible; if it requires work, the opposite holds true.
Additional Notes on Ideal Gases
- For adiabatic compression, initial step results in a final volume of ( 0.008263 , \text{m}^3 ) with a corresponding temperature of ( 462.69 , \text{K} ).
- Work for compression using ( C_V ) is ( W = C_V \Delta T = (20.785)(462.69 - 298.15) = 3420 , \text{J} ).
- In the constant-volume step, no work is done; heat transfer is ( Q = \Delta U_{ig} = 20.785(298.15 - 462.69) = -3420 , \text{J} ).
- Notably, ( Q = -W ) indicates path-dependency, where heat and work are intricately linked in thermodynamic processes.
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