2024 · Paper 1

Complete GATE CH 2024 Paper 1 overview, original pages and practice · Timed previous-paper practice

Questions 55–57 of 65. Imported answers require review unless explicitly marked reviewed.

Question 55

Open question

CHNAT2 marksNeeds review

Methane combusts with air in a furnace as



. The heat of reaction



kJ per mol



and is assumed to be constant. The furnace is well insulated and no other side reactions occur. All components behave as ideal gases with a constant molar heat capacity of 44 J mol



°C



. Air may be considered as 20 mol%



and 80 mol%



. The air-fuel mixture enters the furnace at 50 °C. The methane conversion



varies with the air-to-methane mole ratio,



, as



where



is the stoichiometric air-to-methane mole ratio. For



, the exit gas temperature in °C, rounded off to 1 decimal place, is _____

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Question 56

Open question

CHNAT2 marksNeeds review

An isolated system consists of two perfectly sealed cuboidal compartments A and B separated by a movable rigid wall of cross-sectional area 0.1 m



as shown in the figure. Initially, the movable wall is held in place by latches



and



such that the volume of compartment A is 0.1 m



. Compartment A contains a monoatomic ideal gas at 5 bar and 400 K. Compartment B is perfectly evacuated and contains a massless Hookean spring of force constant 0.3 N m



at its equilibrium length (stored elastic energy is zero). The latches



and



are released, the wall moves to the right by 0.2 m, where it is held at the new position by latches



and



. Assume all the walls and latches are massless. The final equilibrium temperature, in K, of the gas in compartment A, rounded off to 1 decimal place, is ________



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Question 57

Open question

CHNAT2 marksNeeds review

Ethylene obeys the truncated virial equation-of-state



where P is the pressure, V is the molar volume, T is the absolute temperature and B is the second virial coefficient. The universal gas constant



bar cm



mol



K



. At 340 K, the slope of the compressibility factor vs. pressure curve is



bar



. Let



denote the molar residual Gibbs free energy. At these conditions, the value of



, in cm



mol



, rounded off to 1 decimal place, is __________

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