Find the final internal energy of a gas.

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SUMMARY

The final internal energy of a gas in a thermally isolated container, filled with 2.3 mol of an ideal gas at 0°C, is calculated using the formula U = 3/2nRT. During the compression from 1.9 m³ to 0.3 m³ at constant pressure, the work done on the gas is W = pΔV, resulting in a value of -4398.6 J. The correct final internal energy is determined to be 1.24 kJ. The user initially miscalculated the internal energy but later confirmed the correct answer.

PREREQUISITES
  • Understanding of the ideal gas law (pV = nRT)
  • Knowledge of thermodynamic principles, specifically internal energy calculations
  • Familiarity with the concepts of work and heat in thermodynamics
  • Ability to perform calculations involving molar quantities and gas constants
NEXT STEPS
  • Study the derivation and application of the ideal gas law
  • Learn about thermodynamic processes and their impact on internal energy
  • Explore the relationship between work, heat, and internal energy in closed systems
  • Investigate the implications of constant pressure processes on gas behavior
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Students studying thermodynamics, physics enthusiasts, and anyone seeking to understand the behavior of ideal gases under compression.

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Homework Statement


A thermally isolated container is filled with 2.3 mol of an ideal gas at T = 0°C.The gas is then compressed from 1.9 m3 to 0.3 m3. What is the final internal energy U of the gas? (Assume the process occurs at constant pressure.)

Homework Equations


U=3/2nRT
U=Q+W
W=pΔV
pV=nRT


The Attempt at a Solution


Q=0, so U=W

p(1.9)=(2.3)(8.314)(273.15)
p(1.9)=5223.2
p=2749.1

W=pΔV
=(2749.1)(0.3-1.9)
=(2749.1)(-1.6)
=-4398.6

The actual answer is 1.24kJ.

I attempted this as well just to see.

U=3/2nRT
=3/2(2.3)(8.314)(273.15)
=7834.8

Clearly I am lost. Any help would be greatly appreciated.
 
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Nevermind. I got it :D
 

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