Isobaric Process: del(H) = mC(v)dT + (P.dV)/J

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SUMMARY

The discussion focuses on the derivation of the heat transfer (del(H)) in an isobaric process for an ideal gas. It establishes that del(H) can be expressed as del(H) = mC(v)dT + (P.dV)/J, where C(v) is the specific heat at constant volume, P is pressure, and J is the mechanical equivalent of heat. The conclusion drawn is that the difference between the specific heats at constant pressure and volume is given by the equation C(p) - C(v) = r/J, where r is the gas constant. The participants clarify that the internal energy change (dU) is always equal to mC(v)dT, regardless of volume changes.

PREREQUISITES
  • Understanding of thermodynamic processes, specifically isobaric processes.
  • Familiarity with concepts of specific heat capacities, C(p) and C(v).
  • Knowledge of the ideal gas law and its implications.
  • Basic grasp of mechanical equivalents of heat and their significance in thermodynamics.
NEXT STEPS
  • Study the derivation of the ideal gas law and its applications in thermodynamics.
  • Learn about the relationship between internal energy, enthalpy, and work in thermodynamic systems.
  • Explore the implications of the mechanical equivalent of heat in various thermodynamic processes.
  • Investigate the differences between isobaric and isochoric processes in detail.
USEFUL FOR

Students of thermodynamics, physics enthusiasts, and professionals in engineering fields who require a solid understanding of heat transfer in isobaric processes and the behavior of ideal gases.

Amith2006
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Homework Statement



Consider 1 gram of an ideal gas undergoing isobaric process. Suppose del(H) be the amount of heat given to it. Then,
del(H) = dU + del(W)
del(H) = 1 x C(v)dT + (P.dV)/J
But del(H) = C(p)dT
P.dV = r.dT
C(p)dT = C(v)dT + (r.dT)/J
C(p) - C(v) = r/J


Homework Equations





The Attempt at a Solution



In the above derivation, when volume is changing, how can they take dU = mC(v)dT?
Here m = mass of gas,r = gas constant,J = Mechanical equivalent of heat
 
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Amith2006 said:
In the above derivation, when volume is changing, how can they take dU = mC(v)dT?
Here m = mass of gas,r = gas constant,J = Mechanical equivalent of heat
U is a function of temperature only. It does not depend on volume or pressure (although those will affect temperature, of course). dU is always = mC(v)dT

AM
 
That was a nice piece of information.Thanks.
 

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