- 2072 Magh · 4 marks
Heat vs work transfer; isothermal work
Short answer
Heat transfer is boundary energy transfer due only to temperature difference, disorganized; work transfer is from non-thermal potentials, organized. Both are path functions. For an ideal gas isothermal process, work W = P₁V₁ ln(V₂/V₁) = mRT ln(V₂/V₁), derived from W = ∫ P dV with PV = constant.
Differentiate between heat transfer and work transfer. Derive the mathematical expression for work transfer for an isothermal process.
Heat transfer vs work transfer
| Basis | Heat transfer | Work transfer |
|---|---|---|
| Cause | Temperature difference | Force acting through a distance (non-thermal potential) |
| Energy form | Disorganised, microscopic | Organised, macroscopic |
| Conversion | Not fully convertible to work in a cycle | Fully convertible to heat |
| Sign convention | Into system +ve | By system +ve |
| Mode | Conduction, convection, radiation | Boundary, shaft, electrical |
| Property? | No, path function | No, path function |
Work for an isothermal process (ideal gas)
Boundary work W₁₂ = ∫₁² P dV.
For T = constant, PV = mRT = C, so P = mRT/V.
W₁₂ = mRT ∫₁² dV/V = mRT ln(V₂/V₁)
Since P₁V₁ = P₂V₂ = mRT:
W₁₂ = P₁V₁ ln(V₂/V₁) = P₁V₁ ln(P₁/P₂)
Work is positive for expansion (V₂ > V₁) and negative for compression. Because ΔU = 0 for an ideal gas at constant T, the first law gives Q₁₂ = W₁₂.
✓ Answer checked by Claude Opus 5.5 (high effort)
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