GATE CH kind:question PYQs & Answers — Page 51

Questions 501–510 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 51 of 65

The Newton-Raphson method is used to determine the root of the equation

. If the initial guess for the root is 0, the estimate of the root after two iterations is ________ (rounded off to three decimal places).

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Carbon monoxide (CO) reacts with hydrogen sulfide (H₂S) at a constant temperature of 800 K and a constant pressure of 2 bar as:

The Gibbs free energy of the reaction

J/mol and universal gas constant

J/(mol K). Both the reactants and products can be assumed to be ideal gases. If initially only 4 mol of H₂S and 1 mol of CO are present, the extent of the reaction (in mol) at equilibrium is ________ (rounded off to two decimal places).

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For a given binary system at constant temperature and pressure, the molar volume (in m³/mol) is given by:

, where

and

are the mole fractions of components A and B, respectively. The volume change of mixing

(in m³/mol) at

is ________ (rounded off to one decimal place).

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Consider a vessel containing steam at 180 °C. The initial steam quality is 0.5 and the initial volume of the vessel is 1 m³. The vessel loses heat at a constant rate

under isobaric conditions so that the quality of steam reduces to 0.1 after 10 hours. The thermodynamic properties of water at 180 °C are (subscript

: vapor phase; subscript

: liquid phase): specific volume:

m³/kg,

m³/kg; specific internal energy:

kJ/kg,

kJ/kg; specific enthalpy:

kJ/kg,

kJ/kg. The rate of heat loss

(in kJ/hour) is __________ (rounded off to the nearest integer).

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A fractionator recovers 95 mol % n-propane as the distillate from an equimolar mixture of n-propane and n-butane. The condensate is a saturated liquid at 55 °C. The Antoine equation is of the form,

, and the constants are provided below:

Component	A	B	C
n-propane	9.1058	1872.46	−25.16
n-butane	9.0580	2154.90	−34.42

Assuming Raoult’s law, the condenser pressure (in bar) is __________ (rounded off to one decimal place).

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A centrifugal pump is used to pump water (density 1000 kg/m³) from an inlet pressure of 10⁵ Pa to an exit pressure of 2×10⁵ Pa. The exit is at an elevation of 10 m above the pump. The average velocity of the fluid is 10 m/s. The cross-sectional area of the pipes at the pump inlet and outlet is 10⁻³ m² and acceleration due to gravity is

m/s². Neglecting losses in the system, the power (in Watts) delivered by the pump is ________ (rounded off to the nearest integer).

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A solid sphere of radius 1 cm and initial temperature of 25 °C is exposed to a gas stream at 100 °C. For the solid sphere, the density is 10⁴ kg/m³ and the specific heat capacity is 500 J/(kg K). The density of the gas is 0.6 kg/m³ and its specific heat capacity is 10³ J/(kg K). The solid sphere is approximated as a lumped system (Biot number<< 1) and all specific heats are constant. If the heat transfer coefficient between the solid and gas is 50 W/(m² K), the time (in seconds) needed for the sphere to reach 95 °C is __________ (rounded off to the nearest integer).

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Stream A with specific heat capacity

J/(kg K) is cooled from 90 °C to 45 °C in a concentric double pipe counter current heat exchanger having a heat transfer area of 8 m². The cold stream B of specific heat capacity

J/(kg K) enters the exchanger at a flow rate of 1 kg/s and 40 °C. The overall heat transfer coefficient

W/(m² K). Assume that the mean driving force is based on the arithmetic mean temperature difference, that is

where

and

refer to the temperature of the

stream (

) at the inlet and exit, respectively. The mass flow rate of stream A (in kg/s), is __________ (rounded off to two decimal places).

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A 20 cm diameter cylindrical solid pellet of a nuclear fuel with density 600 kg/m³ and conductivity of 300 W/(m K) generates heat by nuclear fission at a spatially uniform rate of 10⁴ W/kg. The heat from the fuel pellet is transferred to the surrounding coolant by convection such that the pellet wall temperature remains constant at 300 °C. Neglecting the axial and azimuthal dependence, the maximum temperature (in °C) in the pellet at steady state is __________ (rounded off to the nearest integer).

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The elementary, irreversible, liquid-phase, parallel reactions, 2A → D and 2A → U, take place in an isothermal non-ideal reactor. The C-curve measured in a tracer experiment is shown in the figure, where

is the concentration of the tracer in g/m³ at the reactor exit at time

(in min).

Diagram for Chemical Engineering question 45

The rate constants are

Liter/(mol min) and

Liter/(mol min). Pure A is fed to the reactor at a concentration of 2 mol/Liter. Using the segregated model, the percentage conversion in the reactor is __________ (rounded off to the nearest integer).

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GATE CH kind:question PYQs

Question 36

Question 37

Question 38

Question 39

Question 40

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Question 44

Question 45