The use of gas turbine engines is the most common way for airplanes to generate thrust. The gas within these engines undergoes a series of thermodynamic processes by which it eventually returns to its original state. Which of the following must be true of the gas turbine engine system once the cycle is complete?
I. The internal energy will have increased.
II. The work done on the system will be equal to the heat added to the system.
III. The pressure and volume will not have changed.
We are told that the gas in a turbine engine undergoes a series of processes, and eventually returns to its initial state. A series of such processes that results in the return to its initial state is known as a Thermodynamic cycle. In returning to the original state, all state variables will be the same at the end of the cycle as they were in the beginning of the cycle.
State variables are variables that describe a given state of a thermodynamic system; they are path independent, meaning that the change in the value of the variable will be the same no matter what path is taken between the initial and final state.
Pressure and volume are both state variables, and thus, statement III is correct. Internal energy is also a state variable. Therefore, there should be no change in internal energy once the cycle is complete. We know that change in internal energy is equal to the heat added to the system plus work done on the system:
ΔU = Q + W
If there is no change in internal energy (since it is a state variable), this means that the heat added, Q, must equal the work done BY the system, -W:
ΔU = Q + W
0 = Q + W
-W = Q
References: Content Review Books, Khan Academy, 100 Most Essential Equations Mastery Course
We are told that the gas in a turbine engine undergoes a series of processes, and eventually returns to its initial state. A series of such processes that results in the return to its initial state is known as a Thermodynamic cycle. In returning to the original state, all state variables will be the same at the end of the cycle as they were in the beginning of the cycle.
State variables are variables that describe a given state of a thermodynamic system; they are path independent, meaning that the change in the value of the variable will be the same no matter what path is taken between the initial and final state.
Pressure and volume are both state variables, and thus, statement III is correct. Internal energy is also a state variable. Therefore, there should be no change in internal energy once the cycle is complete. We know that change in internal energy is equal to the heat added to the system plus work done on the system:
ΔU = Q + W
If there is no change in internal energy (since it is a state variable), this means that the heat added, Q, must equal the work done BY the system, -W:
ΔU = Q + W
0 = Q + W
-W = Q
References: Content Review Books, Khan Academy, 100 Most Essential Equations Mastery Course
We are told that the gas in a turbine engine undergoes a series of processes, and eventually returns to its initial state. A series of such processes that results in the return to its initial state is known as a Thermodynamic cycle. In returning to the original state, all state variables will be the same at the end of the cycle as they were in the beginning of the cycle.
State variables are variables that describe a given state of a thermodynamic system; they are path independent, meaning that the change in the value of the variable will be the same no matter what path is taken between the initial and final state.
Pressure and volume are both state variables, and thus, statement III is correct. Internal energy is also a state variable. Therefore, there should be no change in internal energy once the cycle is complete. We know that change in internal energy is equal to the heat added to the system plus work done on the system:
ΔU = Q + W
If there is no change in internal energy (since it is a state variable), this means that the heat added, Q, must equal the work done BY the system, -W:
ΔU = Q + W
0 = Q + W
-W = Q
References: Content Review Books, Khan Academy, 100 Most Essential Equations Mastery Course