Q. 585.0( 1 Vote )

# Derive the relationship between ΔH and ΔU for an ideal gas. Explain each term involved in the equation.

From the first law of thermodynamics

U = q + W --- (1)

U= internal energy

q= heat absorbed

W= work done

We know W = -pV --- (2)

Therefore we can write equation-1 as

U = q - pV--- (3)

Now if the system absorb qpinternal energy changes from U1 to U2 and volume increase from V1 to V2

U = U2 - U1---(4)

V = V2 - V1 --- (5)

Substitute the value of ∆U and ∆V from equation-4 and equation-5 in equation-3 ie.

U = qp - pV

U2 - U1= qp - p (V2 - V1)

qp = U2 - U1+ p (V2 - V1)

U, P, V are state functions and U + PV is heat content or enthalpy of the system which is denoted by

H = U + PV

So qp = H2 – H1

qp = ∆H

Therefore,H = U + pV--- (6)

At constant temperature when the heat is absorbed, we measure the changes in enthalpy

H = qp (when the heat is absorbed by the system at constant pressure)

H is positive for an endothermic reaction.

H is negative for an exothermic reaction.

At constant volume (V = 0)

U = qv

Therefore,

H = U = qv

Now using ideal gas law if VA is the total volume of gas reactant and VB is the volume of gas product and nA and nB are moles of gas reactant and product respectively.

pVA = nART

pVB = nBRT

Thus, pVB- pVA = nBRT - nART

p(VB – VA) = RT (nB- nA)

pV = ngRT --- (7)

Put the value of pV from equation-7 to equation-5

Therefore,

H = U + ngRT

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Calorimetry - 02 | Mastering important concepts39 mins  Kinetic Theory of Gases46 mins  Enthalpy & Heat Capacity | Interactive Quiz55 mins  Thermodynamics | Types of Enthalpy66 mins  Hess Law61 mins  An interesting lecture on Entropy63 mins  Heat Transfer - 01 | Mastering important concepts40 mins  Interactive Quiz on Gibbs Energy55 mins  Bond Disassociation Enthalpy | Mastering important concepts45 mins  Calorimetry - 01 | Mastering important concepts45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 