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Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - JEE MCQ


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10 Questions MCQ Test Daily Test for JEE Preparation - Test: Kinetic theory-Pressure and Energy of gas (28 Sep)

Test: Kinetic theory-Pressure and Energy of gas (28 Sep) for JEE 2024 is part of Daily Test for JEE Preparation preparation. The Test: Kinetic theory-Pressure and Energy of gas (28 Sep) questions and answers have been prepared according to the JEE exam syllabus.The Test: Kinetic theory-Pressure and Energy of gas (28 Sep) MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Kinetic theory-Pressure and Energy of gas (28 Sep) below.
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Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 1
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The expansion of unit mass of a perfect gas at constant pressure is shown in Fig. Here

Detailed Solution for Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 1
In the given graph, line has a positive slope with the -axis and negative intercept on the -axis.
So we can write the equation of line as
...(i)
According to Charles's law

by rewriting this equation, we get
...(ii)
Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 2
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A gas is heated at a constant pressure. The fraction of heat supplied used for external work is

Detailed Solution for Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 2

We know fraction of given energy that goes to increase the internal energy = 1/γ
So we can say the fraction of given energy that is supplied for external work = 1 − (1/γ).

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Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 3
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Energy of all molecules of a monatomic gas having a volume and pressure is . The total translational kinetic energy of all molecules of a diatomic gas at the same volume and pressure is

Detailed Solution for Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 3
Energy of 1 mol of gas

where degree of freedom
Monatomic or diatomic gases possess equal degree of freedom for translational motion and that is equal to 3 , i.e.,
Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 4
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The average degrees of freedom per molecule for a gas are 6 . The gas performs of work when it expands at constant pressure. The heat absorbed by gas is
Detailed Solution for Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 4
As (given), therefore

Fraction of energy given for extemal work
Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 5
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A gas is filled in the cylinder shown in the figure. The two pistons are joined by a string. If the gas is heated, the pistons will
Detailed Solution for Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 5

When the gas is heated, its temperature increases and thus it expands. As the cross-sectional area of the right piston is more, therefore greater force will work on it (as Force Pressure Area). So the piston will move towards the right.
Option B is correct.

Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 6
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An ideal monatomic gas is confined in a cylinder by a spring-loaded piston of cross-section . Initially the gas is at and occupies a volume of and the spring is in a relaxed state. The gas is heated by a small heater coil The force constant of the spring is and the atmospheric pressure is . The cylinder and piston are thermally insulated The piston and the spring are massless and there is no friction between the piston and cylinder. There is no heat loss through heater coil wire leads and thermal capacity of the heater coil is negligible. With all the above assumptions, if the gas is heated by the heater until the piston moves out slowly by , then the final temperature is
Detailed Solution for Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 6


If area of cross section of piston is A and it moves through distance x, then increment in volume of the gas = Ax.
If force constant of a spring is k, then force F = kx and pressure = F/A = kx/A

Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 7
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Pressure versus temperature graph of an ideal gas of equal number of moles of different volumes is plotted as shown in Fig. Choose the correct alternative.
Detailed Solution for Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 7

From ideal gas equation,

Comparing, this equation with y = mx
Slope of line, tanθ = m = μR/V

It means line of smaller slope represents greater volume of gas.
For the given problem figure

Points 1 and 2 are on the same line, so they will represent same volume, i.e., V1 = V2.
Similarly points 3 and 4 are on the same line, so they will represent same volume, i.e., V3 = V4.
But V1 > V3( = V4) or V2 > V3(=V4) as slope of line

Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 8
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Molar specific heat at constant pressure is related to internal energy and absolute temperature as is equal to
Detailed Solution for Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 8

From Mayer's formula,
Cp − CV = R ⇒ Cp = CV + R
At constant volume, heat capacity,

Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 9
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Forty calories of heat is needed to raise the temperature of 1 mol of an ideal monatomic gas from 20∘C to 30∘C at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume (R = 2calmol−1 K−1) is
Detailed Solution for Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 9

At constant pressure, the amount of heat required is


Thus,


Now

Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 10
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At the top of a mountain a thermometer reads and a barometer reads of . At the bottom of the mountain these read and of , respectively. Ratio of density of air at the top with that of bottom is
Detailed Solution for Test: Kinetic theory-Pressure and Energy of gas (28 Sep) - Question 10
Ideal gas equation, in terms of density,
constant
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