GATE 2026 CH – Question 58
A gas mixture of 50 wt. % argon and 50 wt. % helium flowing through a horizontal tube of uniform diameter at a rate of 1 kg s$^{-1}$ is heated from 300 K to 400 K at 1 bar. Neglect shaft work, and changes in kinetic as well as potential energies between the inlet and the outlet. Assume the mixture exhibits ideal gas behavior. The specific enthalpies of the components are given in the following table.
| Component | Specific enthalpy (kJ kg$^{-1}$) at 300 K | at 400 K |
|---|---|---|
| Argon | 348 | 400 |
| Helium | 1574 | 2092 |
At steady state, the heat input required (in kW) is ___________ (rounded off to the nearest integer).
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Correct answer: 285
Explanation
At steady state with no work and no change in kinetic or potential energy, the heat input equals the enthalpy rise of the stream. For ideal gases the enthalpy of the mixture is the mass weighted sum. Argon: $0.5 \times (400 - 348) = 26$ kW. Helium: $0.5 \times (2092 - 1574) = 259$ kW. The total is $26 + 259 = 285$ kW.