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Wize University Physics Textbook (Master) > Thermodynamics

TS-Diagrams

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T-S curves



For Isochoric Processes:


ΔS=nCv ln⁡ TfTi\displaystyle \Delta S=nC_v\ \ln\ \frac{T_f}{T_i}

→ΔSnCv=ln⁡ TfTi→Tf=TieΔSnCv\displaystyle \to\frac{\Delta S}{nC_v}=\ln\ \frac{T_f}{T_i}\to T_f=T_ie^{\frac{\Delta S}{nC_v}}

Similarly for Isobaric Processes:


Tf=TieΔSnCpT_f=T_ie^{\frac{\Delta S}{nC_p}}

  • 𝐶𝑝 > 𝐶𝑣. So the isochoric line is steeper than the isobaric line

checklist
Mark Yourself Question
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  2. When you're done, check the "I have answered this question" box below.
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A system of a cylinder and a piston has the shape of the diagram below when the temperature of the gas inside the cylinder is 300℃ and its pressure is 200𝐾𝑃𝑎. The piston has a mass of 50 𝑘𝑔 and its radius is . 06 𝑚 and pushes against a set of stops at initial condition so that the height of the cylinder is 80 𝑐𝑚. The temperature outside the cylinder is 30℃ and the pressure is 1 𝑎𝑡𝑚. The cylinder cools down by exchanging heat with the environment.

a. Draw a free body diagram of the piston.

b. At what temperature and pressure does the piston start to move down?

c. How far has the piston dropped when the temperature inside the cylinder reaches the temperature outside the cylinder? (assume the piston moves down with a constant velocity)

d. Draw the PV-Diagram and TS-diagram for the gas to get to the point described in part c.





Extra Practice
A system of a cylinder and a piston has the shape of the diagram below when the temperature of the gas inside the cylinder is 300℃ and its pressure is 200𝐾𝑃𝑎. The piston has a mass of 50 𝑘𝑔 and its radius is . 06 𝑚 and pushes against a set of stops at initial condition so that the height of the cylinder is 80 𝑐𝑚. The temperature outside the cylinder is 30℃ and the pressure is 1 𝑎𝑡𝑚. The cylinder cools down by exchanging heat with the environment.
a. Draw a free body diagram of the piston.
b. At what temperature and pressure does the piston start to move
PV and TS Diagrams
A system of a cylinder and a piston has the shape of the diagram below when the temperature of the gas inside the cylinder is 300℃ and its pressure is 200𝐾𝑃𝑎. The piston has a mass of 50 𝑘𝑔 and its radius is . 06 𝑚 and pushes against a set of stops at initial condition so that the height of the cylinder is 80 𝑐𝑚. The temperature outside the cylinder is 30℃ and the pressure is 1 𝑎𝑡𝑚. The cylinder cools down by exchanging heat with the environment.
a. Draw a free body diagram of the piston.
b. At what temperature and pressure does the piston start to move down?
Entropy: Heat Engines
A cylinder contains a diatomic gas at a pressure of 3 atm and a temperature of 250K. Its initial volume is 4.0 liters. The gas is next carried through the following processes:
a. It is expanded isobarically to a temperature of 375K.
b. It is cooled down to 250K in an isochoric process.