How Does Heating Affect the Internal Energy of Gas in a Piston-Cylinder System?

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SUMMARY

The discussion focuses on calculating the change in internal energy of a gas in a piston-cylinder system when heated from 300K to 400K. The heat capacity at constant pressure is given as 500 J/K, and the weight on the piston is 10,000N. The user initially calculated heat transfer (Q) as 50,000 J but faced challenges determining the work done (W) and ultimately the change in internal energy (ΔU). The correct approach involves using the equation ΔU = Q - W, where W is derived from the pressure of the system and the change in volume.

PREREQUISITES
  • Understanding of the first law of thermodynamics
  • Knowledge of heat capacity and its application in thermodynamic calculations
  • Familiarity with piston-cylinder systems and gas laws
  • Basic principles of pressure and work in thermodynamic systems
NEXT STEPS
  • Study the first law of thermodynamics and its applications in closed systems
  • Learn about the calculation of work done by gases in piston-cylinder systems
  • Explore the concept of heat capacity and its role in energy transfer
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USEFUL FOR

Students and professionals in thermodynamics, mechanical engineers, and anyone involved in the study of gas behavior in piston-cylinder systems will benefit from this discussion.

huskydc
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A cylinder (cross section is 0.2m2) with a free moving piston is filled with gas. The piston is attached to a heavy weight W = 10000N. Outside the cylinder, the air is at 300K and 1atm. Initially the gas is at 300K, then it is heated to 400K. The heat capacity of the gas under the constant pressure is 500J/K.
If the length of the gas in the cylinder l increases by 20cm during the heating, find the change in the internal energy of the gas in Joule J.



i figured...heat is being transferred to the gas, and work is done by the gas, so both Q and W should be positive...

delta U = Q - W

i'm not really sure how to start this...but i tried the following:

C = Q/ delta T

500 = Q / (400-300)

Q = 50000 J

W = P delta V (i'm not sure if the P is of the system or the surrounding)

but with the problem, I've been given a clue that says this:

P system = (P surrounding - W force)/cross area...

and I came up with 456500 J...

Q- W

50000 - 456500 = delta U...apparently the answer didn't work, any clues?
 

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:frown: :frown: can i even use the equation: delta U = 1.5 n R delta T
but that would include finding out n...which i don't have enough info to calculate...any one help??
i'm lost... =(
 
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