GATE XE format:mcq PYQs & Answers — Page 42

Questions 411–420 of 959. Imported answers require independent review unless marked reviewed.

A rectangular plate of uniform thickness having initial length

and width

is placed between two rigid immovable walls. The temperature of the plate is increased by

. The plate is free to expand along the

and

directions. The mid-surface of the plate remains in the

-plane. The Poisson’s ratio is

and the coefficient of thermal expansion is

. Assuming that the plate is initially free of stresses, the change in length of the plate after the increase in temperature is given by

Diagram for Engineering Sciences question 79

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A mass

kg is attached to a spring as shown in the figure. The coefficient of friction between the mass and the inclined plane is 0.25. Assume that the acceleration due to gravity is 10 m/s

and that static and kinetic friction coefficients are the same. Equilibrium of the mass is impossible if the spring force is

Diagram for Engineering Sciences question 80

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30 N

45 N

60 N

75 N

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The energy equation for a reversible non-flow process can be expressed as

, where

is the heat transfer per unit mass,

is the internal energy per unit mass,

is the pressure, and

is the mass specific volume. This energy equation is not in exact differential form. It can be made exact differential by multiplying with the following integrating factor: (T is the absolute temperature)

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An air standard Diesel cycle consists of four processes: 1-2 (isentropic compression), 2-3 (constant pressure heat addition), 3-4 (isentropic expansion) and 4-1 (constant volume heat rejection).

is the temperature (in K) attained at the end of isentropic expansion (3-4) before constant volume heat rejection. The constant volume heat rejection process (4-1) is replaced by a constant pressure heat rejection process (4a-1) such that

is the temperature (in K) reached at the end of isentropic expansion (3-4a), and the state point 1 remains the same. Then

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Gas in a cylinder-piston device expands from state 1

to state 2

. The expansion process is polytropic, i.e.,

. Assuming the ideal gas behaviour, the expression for the work done,

by the system is given by

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The temperature of the working fluid in a real heat engine cycle changes during heat addition and heat rejection processes. The maximum and minimum temperatures of the cycle are

and

, respectively. If

is the thermal efficiency of a Carnot engine operating between these temperature limits, then the thermal efficiency,

of the real heat engine satisfies the relation

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One of the Maxwell equations is expressed as

, where

is the entropy per unit mass,

is the mass specific volume,

is the pressure, and

is the temperature. In this expression,

is a continuous function of

and

. The derivatives of

are also continuous. Let

be specific heat capacity at constant volume for a gas. Then,

can be written as

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The general relation among the properties

and

at any state point can be expressed as

. If

and

are continuous functions and

is the Joule-Thomson coefficient, then

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An air-conditioning system consists of an insulated rigid mixing chamber designed to supply air at 24 °C to a building. The mixing chamber mixes two air streams: (i) a cold air stream at 10 °C and mass flow rate

(kg/s), and (ii) a stream of fresh ambient air at 30 °C and mass flow rate

(kg/s). Assume air to be an ideal gas with constant specific heat (

kJ/(kg K),

). Neglect change in kinetic and potential energies as compared to change in enthalpy. Under the steady state condition, the ratio of the mass flow rates of the two streams (

) is

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An ideal gas mixture consists of 80% N₂ and 20% O₂ on mass basis. If the total pressure is 300 kPa, then the partial pressure of N₂ (in kPa) is

(Molecular weights of N₂ = 28 kg/kmol and O₂ = 32 kg/kmol)

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246.15

230.34

254.78

213.54

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GATE XE format:mcq PYQs

Question 79

Question 80

Question 88

Question 89

Question 90

Question 91

Question 97

Question 98

Question 99

Question 100