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Wize University Physics Textbook (Master) > Thermodynamics

Thermodynamic Cycles

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Thermodynamic Cycles

  • A thermodynamic cycle is a closed loop in a PV-diagram.
  • The system starts with some internal thermal energy U at the beginning of the cycle and returns to the same state with the same internal thermal energy (∆T=0).
  • Thus ∆U = 0 for any thermodynamic cycle.
ΔU=Q−W=0→Q=W\Delta U=Q-W=0\to Q=W

  • The total work done during a thermodynamic cycle is the sum of the work done in each process within the cycle.
  • The total work is equivalent to the area enclosed by the cycle.
  • If the cycle is clockwise, 𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 by 𝑡ℎ𝑒 𝑔𝑎𝑠 is Positive
  • If the cycle is counter-clockwise, 𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 by 𝑡ℎ𝑒 𝑔𝑎𝑠 is Negative
An ideal gas has an initial pressure of 20 Pa and a volume of 1 m3 as shown below. It is expanded to a final volume of 3 m3 and a final pressure of 5 Pa. Determine the heat energy transferred to/from the gas.



Q = W + Δ U

W = P ΔV
= Area under the curve
= Areatriangle + Arearectangle
= 1/2 b h1 + b h2
= 1/2 (2)(15) + (2)(5)
= 25 J

Δ U = 3/2 n R T
= 3/2 ΔP ΔV = 3/2 Pf Vf - 3/2 Pi Vi
= 3/2(5)(3) - 3/2(20)(1)
= - 7.5 J

Q = W + Δ U
= 25 - 7.5 = 17.5 J
0.5 mole of a gas undergoes a cycle shown below. Find the heat has been added/removed from the gas during this cycle?
Extra Practice
Thermodynamic Cycle (PV Diagram)
0.5 mole of a gas undergoes a cycle shown below. Find the heat has been added/removed from the gas during this cycle?
New Practice Question
An engineer wants to design! A thermodynamic path in order to increase the temperature of 1000 lit of a diatomic gas from 350K to 850K. He is considering two different options. The first method is to increase the temperature using a series of alternating adiabatic and isothermal processes so that during each adiabatic process the gas is heated up by 100K and then is expanded to its original volume through an isothermal process. The second method is to raise the temperature through a single isochoric process.
a) Draw P-V and T-S curves for both methods
b) In which method the heat added to the gas is less?
Thermodynamics: Heat Engines
A diatomic gas undergoes some thermodynamical processes according to the following plot. Imagine the process from a to b could be changed in order to get different efficiency for the following cycle under the condition that the temperature of the gas cannot exceed the temperature at point a during the entire cycle. What is the work done by the gas from a to b in a process which makes the efficiency of the heat engine equal to the half of the efficiency of a Carnot engine which works in the same range of temperatures? (Assume we have 2 moles of the gas)
The internal energy of a system remains constant during
cyclic
process.
Heat engine
A reversible heat engine has a pV diagram shown on the graph. Determine the net heat transferred between the engine and environment in one cycle.