Internal energy change in isobaric system

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SUMMARY

The discussion centers on the internal energy change (ΔU) and work done (W) in an isobaric system, specifically during the compression of an ideal gas. The first law of thermodynamics is applied, stating ΔQ = ΔU + W, where W is defined as PΔV. The relationship between specific heat capacity at constant pressure (Cp) and internal energy change is explored, emphasizing that for an ideal gas, ΔU is a function of temperature change (ΔT) and can be expressed in terms of Cp and ΔT.

PREREQUISITES
  • Understanding of the first law of thermodynamics
  • Familiarity with ideal gas laws
  • Knowledge of specific heat capacities (Cp and Cv)
  • Concept of isobaric processes in thermodynamics
NEXT STEPS
  • Study the derivation of the first law of thermodynamics in isobaric processes
  • Learn about the relationship between internal energy (ΔU) and temperature change (ΔT) for ideal gases
  • Explore the mathematical relationship between specific heat capacities (Cp and Cv)
  • Investigate the implications of quasi-static processes in thermodynamic systems
USEFUL FOR

Students and professionals in thermodynamics, mechanical engineers, and anyone studying the behavior of gases under isobaric conditions.

cooper607
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hi all, i have a confusion about the internal energy change and work done in a isobaric system...
suppose i want to find the delQ in isobaric system in terms of P & V...now i may assume the delW part would be pdv=p(V2-V1)...as i m compressing the gas...
but what happens to the du?
and is the specific heat capacity at const pressure somehow related to the du?
please help
 
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cooper607 said:
hi all, i have a confusion about the internal energy change and work done in a isobaric system...
suppose i want to find the delQ in isobaric system in terms of P & V...now i may assume the delW part would be pdv=p(V2-V1)...as i m compressing the gas...
but what happens to the du?
and is the specific heat capacity at const pressure somehow related to the du?
please help
Use the first law:

ΔQ = ΔU + W where W is the work done by the system.

If the compression is slow enough, you could treat it as a quasi-static isobaric compression such that W = PΔV.

To find ΔQ all you have to do is find ΔU. If this is an ideal gas, that is easy to do because ΔU is related to ΔT (how?) and ΔT is related to Δ(PV) by the ideal gas law. Or you could just use Cp and the change in T to determine ΔQ.

AM
 
well as for ideal gas U is only function of T, so i think we can replace dU with dT...but i just don't want to split the delQ here...
so i wanted to know is there any direct link between Cp and dU so that somehow i can replace the dU in terms of Cp & dT?
 
cooper607 said:
well as for ideal gas U is only function of T, so i think we can replace dU with dT...but i just don't want to split the delQ here...
so i wanted to know is there any direct link between Cp and dU so that somehow i can replace the dU in terms of Cp & dT?
What is the relationship between ΔU and ΔT (for an ideal gas? What is the relationship between Cv and Cp?

AM
 

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