Class 11 Physics

Chapter 11 Solutions — Thermodynamics

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Solutions

Overview

Step-by-step NCERT solutions for Thermodynamics (Chapter 11, NCERT Class 11 Physics) — every question and answer worked out in full, not just the final result. You can also read the Thermodynamics textbook chapter.

Solved

What these solutions cover

All 8 questions in Thermodynamics are solved in the PDF. Here's what's inside, exercise by exercise:

Exercises

A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is 4.0 × 10⁴ J/g?
What amount of heat must be supplied to 2.0 × 10⁻² kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass of N2 = 28; R = 8.3 J mol⁻¹ K⁻¹.)
3.
Explain why
- (a) Two bodies at different temperatures T1 and T2 if brought in thermal contact do not necessarily settle to the mean temperature (T1 + T2)/2.
- (b) The coolant in a chemical or a nuclear plant (i.e., the liquid used to prevent the different parts of a plant from getting too hot) should have high specific heat.
- (c) Air pressure in a car tyre increases during driving.
- (d) The climate…
A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?
In changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state B, an amount of work equal to 22.3 J is done on the system. If the gas is taken from state A to B via a process in which the net heat absorbed by the system is 9.35 cal, how much is the net work done by the system in the latter case? (Take 1 cal = 4.19 J)
6.
Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following:
- (a) What is the final pressure of the gas in A and B?
- (b) What is the change in internal energy of the gas?
- (c) What is the change in…
An electric heater supplies heat to a system at a rate of 100 W. If the system performs work at a rate of 75 joules per second, at what rate is the internal energy increasing?
A thermodynamic system is taken from an original state to an intermediate state by the linear process shown in Fig. 11.11. Its volume is then reduced to the original value from E to F by an isobaric process. Calculate the total work done by the gas from D to E to F.

Sample

Worked examples

3 questions from Thermodynamics, solved step by step.

Exercises

A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is 4.0 × 10⁴ J/g?

Given:

Flow rate of water = 3.0 L/min = 3.0 kg/min (density of water ≈ 1 kg/L)

Initial temperature T1 = 27 °C, final temperature T2 = 77 °C

Temperature rise ΔT = 77 - 27 = 50 °C = 50 K

Specific heat of water c = 4186 J kg⁻¹ K⁻¹

Heat of combustion of fuel H = 4.0 × 10⁴ J/g

Heat required per minute to warm the water:

Q = m × c × ΔT = 3.0 × 4186 × 50 = 627 900 J/min

All this heat must come from burning the fuel. If the fuel consumption rate is r g/min:

r × H = Q

r = Q / H = 627 900 / (4.0 × 10⁴) ≈ 15.7 g/min

Answer: Rate of fuel consumption ≈ 15.7 g/min

Exercises

What amount of heat must be supplied to 2.0 × 10⁻² kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass of N2 = 28; R = 8.3 J mol⁻¹ K⁻¹.)

Given:

Mass of nitrogen m = 2.0 × 10⁻² kg = 20 g

Molecular mass M = 28 g/mol

Temperature rise ΔT = 45 °C = 45 K

Process: constant pressure

R = 8.3 J mol⁻¹ K⁻¹

Number of moles:

μ = m / M = 20 / 28 = 5/7 ≈ 0.714 mol

N2 is a diatomic molecule. At room temperature only translational and rotational degrees of freedom are active (f = 5), so:

Cv = (5/2) R and Cp = Cv + R = (7/2) R

Cp = (7/2) × 8.3 = 29.05 J mol⁻¹ K⁻¹

Heat at constant pressure:

Q = μ × Cp × ΔT = (5/7) × 29.05 × 45

Q = 0.7143 × 29.05 × 45 ≈ 933.8 J

Answer: Q ≈ 933.8 J ≈ 9.34 × 10² J

Exercises

A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

Given:

Gas: H2 (diatomic), μ = 3 mol

Walls and piston are heat-insulating ⇒ adiabatic compression

Final volume V2 = V1/2

For an adiabatic process of an ideal gas:

P V^γ = constant ⇒ P1 V1^γ = P2 V2^γ

H2 is diatomic; at room temperature (rotational modes active, vibrational modes not):

Cv = (5/2) R, Cp = (7/2) R

γ = Cp / Cv = 7/5 = 1.4

Pressure ratio:

P2 / P1 = (V1 / V2)^γ = (V1 / (V1/2))¹.4 = 2¹.4

2¹.4 = 2^(7/5) = (2⁷)^(1/5) = 128⁰.2 ≈ 2.639

Answer: The pressure increases by a factor of 2¹.4 ≈ 2.64

All 8 questions in Thermodynamics are solved step by step in the Solutions PDF above.

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Chapter 11 Solutions — Thermodynamics

Overview

What these solutions cover

Exercises

Worked examples

A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is 4.0 × 10⁴ J/g?

What amount of heat must be supplied to 2.0 × 10⁻² kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass of N2 = 28; R = 8.3 J mol⁻¹ K⁻¹.)

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