Thermodynamics

01

PYQ 2020

medium

physics ID: mht-cet-

One mole of a diatomic gas does a work, when the amount of heat supplied is . In this process, the molar heat capacity of the gas is}

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Official Solution

Correct Option: (1)

$Step 1: Relation for molar heat capacity. The work done by the gas is related to the heat supplied by: The first law of thermodynamics gives: For a diatomic gas, the change in internal energy is: Step 2: Using the given information. The total heat supplied . For one mole of gas, this becomes: Substitute into the first law: Step 3: Solving for . By solving the equation, we find that: Step 4: Conclusion. The molar heat capacity is .$

02

PYQ 2020

medium

physics ID: mht-cet-

$The initial pressure and volume of a gas is and respectively. First, by isothermal process, gas is expanded to volume, and then by adiabatic process its volume is compressed to . Then its final pressure is (Ratio of specific heat at constant pressure to constant volume)$

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$6P$

2

$27P$

3

$3P$

4

$9P$

Official Solution

Correct Option: (3)

$Step 1: Understand the isothermal process. In the isothermal process, the temperature remains constant. The equation for an isothermal expansion is: Here,,, and . After expansion: Step 2: Apply the adiabatic process. In an adiabatic process, the relationship between pressure and volume is given by: Here,, and . Using : Simplifying: Step 3: Conclusion. Thus, the final pressure is, which corresponds to option (C).$

03

PYQ 2020

medium

physics ID: mht-cet-

$A thin uniform rod has mass and length . The moment of inertia about an axis perpendicular to it and passing through the point at a distance from one of its ends, will be$

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Official Solution

Correct Option: (3)

$Step 1: Moment of inertia formula. For a thin uniform rod, the moment of inertia about an axis perpendicular to it and passing through one of its ends is: However, the axis of rotation is at a distance from the end, not the center. Step 2: Use of parallel axis theorem. Using the parallel axis theorem, the moment of inertia about an axis a distance from the center is: For this case,, so: Step 3: Conclusion. The moment of inertia is, so the correct answer is (C) .$

04

PYQ 2020

medium

physics ID: mht-cet-

$A molecule consists of two atoms each of mass and separated by a distance . At room temperature the average rotational kinetic energy is, then its angular frequency is$

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Official Solution

Correct Option: (1)

$Step 1: Understanding the relation. The angular frequency for a rotating molecule is related to the rotational kinetic energy by the formula: where is the moment of inertia. For a diatomic molecule,, where is the reduced mass and is the distance between the atoms. Step 2: Using the given values. Substitute and, and solve for the angular frequency . After simplification, we obtain: Step 3: Conclusion. Thus, the angular frequency is, which corresponds to option (A).$

05

PYQ 2020

medium

physics ID: mht-cet-

$If is the amount of heat supplied to moles of a diatomic gas at constant pressure, is the change in internal energy and is the work done, then is$

1

$2:3:4$

2

$1:2:3$

3

$2:5:7$

4

$5:7:9$

Official Solution

Correct Option: (3)

$Step 1: First law of thermodynamics. From the first law of thermodynamics, we know: For a diatomic gas at constant pressure: Where: - and are the specific heats at constant pressure and volume, respectively. - For a diatomic gas, and . Step 2: Applying the relation. We know that: Thus, the correct answer is (C) 2:5:7 .$

06

PYQ 2020

medium

physics ID: mht-cet-

$Heat is applied to a rigid diatomic gas at constant pressure. The ratio is$

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Official Solution

Correct Option: (2)

$Step 1: Degrees of freedom of diatomic gas. For a rigid diatomic gas, degrees of freedom Step 2: Write expressions for thermodynamic quantities. At constant pressure, Step 3: Use values of and . Step 4: Write ratio. Step 5: Simplify ratio. Step 6: Conclusion. The correct ratio is .$

07

PYQ 2022

easy

physics ID: mht-cet-

$What is intensive property?$

Official Solution

Correct Option: (1)

$An intensive property is a physical or chemical property of a substance that does not depend on the amount or size of the sample being examined. In other words, it is a property that remains constant regardless of the quantity of the substance. Intensive properties are often used to characterize and identify substances. Examples of intensive properties include: Density: Density is the mass of a substance per unit volume. It is an intensive property because it remains constant regardless of the amount of the substance present. Temperature: Temperature is a measure of the average kinetic energy of the particles in a substance. It is an intensive property because it is independent of the quantity of the substance. Melting point: The melting point is the temperature at which a substance changes from a solid to a liquid state at atmospheric pressure. It is an intensive property because it is the same for a given substance regardless of the amount. Color: Color is an intensive property because it does not change with the amount of the substance. For example, a small piece of gold will have the same color as a larger piece of gold. Boiling point: The boiling point is the temperature at which a substance changes from a liquid to a gas at atmospheric pressure. Like the melting point, it is an intensive property.$

08

PYQ 2024

medium

physics ID: mht-cet-

$A real gas within a closed chamber at undergoes the cyclic process as shown in the figure. The gas obeys the equation for the path A to B. The net work done in the complete cycle is (assuming):$

1

$225 J$

2

$205 J$

3

$20 J$

4

Official Solution

Correct Option: (2)

$The cyclic process includes three distinct stages: AC (isochoric process), BC (isobaric process), and AB (defined by). Step 1: Isochoric process (AC) In an isochoric process, the volume remains constant, so no work is done: Step 2: Isobaric process (BC) The work done in an isobaric process is calculated using: Step 3: Process AB () The work done in this process is: Substitute and : Simplify the expression: Substitute and : Net Work Done: The total work done is the sum of work from all segments of the process: Final Answer:$

09

PYQ 2024

medium

physics ID: mht-cet-

$A mixture of one mole of monoatomic gas and one mole of diatomic gas (rigid) are kept at room temperature (). The ratio of specific heat of gases at constant volume respectively is:$

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Official Solution

Correct Option: (3)

$The specific heat capacity at constant volume () depends on the degrees of freedom of a gas: - For a monoatomic gas: where is the universal gas constant. - For a rigid diatomic gas (no vibrational degrees of freedom): Step 1: Calculate the Ratio of Specific Heats The ratio of specific heat capacities for the monoatomic and diatomic gases is: Simplify: Final Answer:$

10

PYQ 2024

medium

physics ID: mht-cet-

$Two vessels and are of the same size and are at the same temperature. Vessel contains of hydrogen and vessel contains of oxygen. and are the pressures of the gases in and respectively. Then is:$

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Official Solution

Correct Option: (2)

$The ideal gas equation relates pressure, volume, temperature, and the number of moles: where is the number of moles of gas. Step 1: Determine the Number of Moles For hydrogen (): For oxygen (): Step 2: Compute the Ratio of Pressures Since : Simplify: Final Answer:$

11

PYQ 2024

medium

physics ID: mht-cet-

$A cylinder of fixed capacity contains helium gas at STP. The amount of heat needed to raise the temperature of the gas in the cylinder by is:$

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Official Solution

Correct Option: (2)

$Step 1: Recall the formula for heat capacity at constant volume. The heat required to raise the temperature of a gas is given by: where: is the number of moles of gas, is the molar heat capacity at constant volume for helium, is the temperature change. Step 2: Calculate the number of moles. At STP (Standard Temperature and Pressure), the molar volume of an ideal gas is . The number of moles is: Step 3: Substitute the known values. For helium,, where : The temperature change is . Substitute these into the formula: Step 4: Calculate the result. Thus, the heat required is .$

12

PYQ 2025

easy

physics ID: mht-cet-

$A gas absorbs of heat while performing of work on its surroundings. Calculate the change in internal energy of the gas.$

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Official Solution

Correct Option: (1)

$According to the first law of thermodynamics, the change in internal energy is given by the formula: Where: - is the heat absorbed by the gas, - is the work done by the gas on its surroundings. Substituting the known values: Thus, the change in internal energy of the gas is .$

13

PYQ 2025

medium

physics ID: mht-cet-

$A gas expands from a volume of 2 m to a volume of 5 m at a constant pressure of . Calculate the work done by the gas.$

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Official Solution

Correct Option: (1)

$The work done by a gas during an isobaric (constant pressure) expansion is given by: Where: - is the pressure, - is the change in volume. Substituting the values: Thus, the work done by the gas is .$

14

PYQ 2025

easy

physics ID: mht-cet-

$In adiabatic compression, which of the following is true?$

1

$Temperature increases$

2

$Temperature decreases$

3

$Pressure remains constant$

4

$Amount of heat exchanged with surround$

Official Solution

Correct Option: (1)

$In adiabatic compression, there is no heat exchange with the surroundings. The work done on the gas compresses it, increasing its internal energy and thus raising its temperature.$

15

PYQ 2026

easy

physics ID: mht-cet-

$A gas having and volume 360 cc is suddenly compressed to 90 cc. If the initial pressure of the gas is, find the final pressure.$

Official Solution

Correct Option: (1)

$Step 1: Understanding the Concept: A "sudden" compression indicates an adiabatic process, where no heat exchange occurs with the surroundings. For an adiabatic process, the relationship between pressure and volume is . Step 2: Key Formula or Approach: Step 3: Detailed Explanation: Given: Initial Pressure . Initial Volume cc. Final Volume cc. Adiabatic index . 1. Calculate the volume ratio: 2. Substitute into the formula: 3. Solve the power: . Step 4: Final Answer: The final pressure is .$

16

PYQ 2026

easy

physics ID: mht-cet-

$Find the heat energy that must be supplied to 14 g of nitrogen at room temperature to raise its temperature by at constant pressure. (Molecular weight of nitrogen = 28; is the gas constant; for a diatomic gas.)$

Official Solution

Correct Option: (1)

$Step 1: Understanding the Concept: The heat energy supplied at constant pressure is given by, where is the number of moles and is the change in temperature. Step 2: Key Formula or Approach: 1. Number of moles . 2. . Step 3: Detailed Explanation: 1. Calculate moles (): mol. 2. Given parameters: . C (Note: a change of C is equal to a change of 48 K). 3. Calculate Heat (): Step 4: Final Answer: The heat energy required is .$

High-Yield Trend

Chapter Questions
16 MCQs

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Thermodynamics

High-Yield Trend

Chapter Questions 16 MCQs

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Chapter Questions
16 MCQs