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What is the actual work done during mechanically reversible, adiabatic compression when the process has an efficiency of 80%?
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%?
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?
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?
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?
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?
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%?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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)?
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?
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?
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?
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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