How can you transform the equation to calculate delta U from delta H?

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SUMMARY

The discussion centers on the transformation of the equation ΔH = ΔU + Δ(PV) into various forms, specifically ΔH = ΔU + nRΔT. It is established that this transformation is valid only when the number of moles (n) remains constant. The participants also explore calculating ΔU, ΔS, and ΔH for the phase transition of 1 mole of liquid water at 25°C and 1 atm to 1 mole of steam at 100°C and 1 atm, emphasizing the importance of recognizing that ΔH already accounts for temperature changes.

PREREQUISITES
  • Understanding of thermodynamic equations, specifically ΔH and ΔU.
  • Familiarity with the ideal gas law and the concept of nRT.
  • Knowledge of phase transitions and their associated thermodynamic properties.
  • Basic calculus for manipulating equations involving derivatives.
NEXT STEPS
  • Study the derivation of the relationship between ΔH and ΔU in thermodynamics.
  • Learn about the implications of constant n in thermodynamic equations.
  • Explore the calculation of ΔS for phase transitions and its relation to ΔH and ΔU.
  • Investigate the application of the ideal gas law in real-world thermodynamic problems.
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Students and professionals in chemistry and thermodynamics, particularly those involved in calculating thermodynamic properties during phase changes and energy transformations.

p3t3r1
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So the equation

\Delta H = \Delta U + \Delta (PV)<br /> <br />

I know you can transform this equation into the form


\Delta H = \Delta U + \Delta (nRT)<br /> <br />

I commonly see the previous equation transferred into the following


\Delta H = \Delta U + \Delta n(RT)<br />

What I want to know is.. can you transform it into

\Delta H = \Delta U + nR \Delta T<br />
 
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p3t3r1 said:
What I want to know is.. can you transform it into

\Delta H = \Delta U + nR \Delta T<br />

I'd say so. But only if n is constant. What are you trying to do?
 
It was really in relation to this problem

Calculate the values of delta U, delta S, and delta H for the following process

1 mole of liquid water at 25 c and 1 atm to 1 mole of steam at 100 c and 1 atm

I figured out the delta H for the entire process.

then I tried to figure out delta U from delta H using the relationship

delta H = delta U + delta (nRT)

See the thing is... delta H I figured out is for the entire process (temperature rise and state change) and I forget about that.. so I was tryign to get the equation into the form

delta H = delta U + n x delta T x R

but that isn't right since delta H already included the delta T variable. and n is really delta n = 1 since I generated 1 mole of gas.

so yeah all I had to do was times it by T to the right answer
 

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