Adiabatic Process Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. For the adiabatic process to take place, the system should be ______.

1. Perfectly insulating
2. Perfectly conducting
3. Semi-insulating
4. Semiconducting

Ans. The correct answer is a. Perfectly insulating

Explanation: The system must be perfectly isolated from its surroundings in order for the adiabatic process to take place.

Ques. In the adiabatic process, transformation is ______.

1. Slow
2. Fast
3. Zero
4. None of the above

Ans. The correct answer is b. Fast

Explanation: In the adiabatic process, the transfer of heat is very fast.

Ques. _______ is the ideal behavior for a closed system, in which the pressure is constant, and the temperature is decreasing.

1. Adiabatic constant
2. Adiabatic compression
3. Adiabatic expansion
4. None of the above

Ans. The correct answer is b. Adiabatic compression

Explanation: The pressure remains constant as the temperature decreases in adiabatic compression.

Ques. The ratio of heat capacity at constant pressure to heat capacity at constant volume gives ______.

1. Efficiency index
2. Isothermal index
3. Compression index
4. Adiabatic index

Ans. The correct answer is d. Adiabatic index

Explanation: The ratio of heat capacity at constant pressure to heat capacity at constant volume is given by the adiabatic index.

Ques. A pendulum oscillating in a vertical plane is an example of the adiabatic process.

1. True
2. False

Ans. The correct answer is a. True

Explanation: A pendulum oscillating in a vertical plane is an example of an adiabatic process since there is no heat transfer between the system and its surroundings.

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Short Answers Questions [2 Marks Questions]

Ques. Define adiabatic process.

Ans. The adiabatic process is a thermodynamic process in which no heat is exchanged from the system to its surroundings during expansion or contraction.

Ques. What is the formula to represent the adiabatic process?

Ans. The formula for an adiabatic process of an ideal gas is given by

PV^γ = constant

Where

• P is the pressure of the gas
• V is the volume of the gas
• γ is adiabatic index

Ques. What is an adiabatic index?

Ans. The adiabatic index, commonly known as the heat capacity ratio in thermal physics and thermodynamics, is the ratio of heat capacity at constant pressure (C_P) to heat capacity at constant volume (C_V). It is commonly referred to as the isentropic expansion factor and is indicated by γ (gamma) for an ideal gas or k (kappa) for a real gas.

Ques. What is meant by the isothermal process?

Ans. A thermodynamic process in which the temperature of a system remains constant is known as an isothermal process. Heat is transferred into and out of the system at such a slow rate that thermal equilibrium is maintained. The Isothermal Process describes the change of a substance, object, or system at a constant temperature.

Also Read:

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Long Answers Questions [3 Marks Questions]

Ques. What is the difference between adiabatic and isothermal processes?

Ans. The differences between the adiabatic and isothermal processes are

Ques. What are the essential conditions for the adiabatic process to take place? Write the formula for work done in an adiabatic process.

Ans. The essential conditions for the adiabatic process to take place are

• The system must be perfectly isolated from its surroundings.
• The process should be completed fast to provide enough time for the transfer of heat to occur.

Work done in the adiabatic process is given by

\(W = \frac{\mu R (T_2-T_1)}{ \gamma -1}\)

Where

• µ is the number of moles of the gas
• R is universal gas constant
• T₁ and T₂ are the initial and final temperatures
• γ is adiabatic index

Ques. What are the examples of the adiabatic process?

Ans. Examples of the adiabatic processes are

• It is a process in which gas is compressed and heat is produced. One of the most basic examples is the discharge of air from a pneumatic tire.
• Adiabatic Efficiency is used to describe the performance of equipment such as nozzles, compressors, and turbines. One of the best uses of the adiabatic process.
• One example is a pendulum oscillating on a vertical plane.
• An adiabatic system is also a quantum harmonic oscillator.
• When we place the ice in the icebox, no heat is lost or gained.

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Very Long Answers Questions [5 Marks Questions]

Ques. The pressure (1 x 10⁵ N/m²) of the air filled in a vessel is decreased adiabatically so much as to increase its volume three times. Calculate the pressure of air. γ for air = 1.4, log₁₀ 3 = 0.4771, and log₁₀ 2.148 = 0.33206.

Ans. Let

• P₁ be the initial pressure
• P₂ be the final pressure
• V₁ be the initial volume
• V₂ be the final volume

Given

• The initial pressure of the air filed in the vessel is, P₁ = 1 x 10⁵ N/m²
• Final volume, V₂ = 3V₁

For adiabatic expression, we have PV^γ = constant, therefore

P₁V^γ₁ = P₂V^γ₂

On substituting the values, we get

1 x 10⁵ x V^γ₁ = P₂ (3V₁)^γ

⇒ P₂ = 10⁵/3^γ

Given γ for air = 1.4, therefore

P₂ = 10⁵/3^1.4

Taking log in both sides, we get

log P₂ = log 10⁵ - log 3^1.4

On solving, we get

P₂ = 2.148 x 10⁴ N/m²

Ques. A tire pumped to a pressure of 3.375 atmospheres and at 27 ℃ suddenly bursts. What is the final temperature? (γ = 1.5)

Ans. Given

• Initial pressure, P₁ = 3.375 atmosphere
• Final pressure, P₂ = 1 atmosphere
• Initial temperature, T₁ = 27 ℃ = 27 + 273 = 300 K
• Final temperature, T₂ = ?

The air of the tyre is adiabatically expanded. Therefore from adiabatic expression, we have

PV^γ = constant

But from the ideal gas equation, for one mole of the ideal gas, we have PV = RT

⇒ V = RT/P

Therefore adiabatic expression becomes

P(RT/P)^γ = constant

⇒ T^γ/P^γ-1 = constant

⇒ T₁^γ/P₁^γ-1 = T₂^γ/P₂^γ-1

⇒ (T₁/T₂)^γ = (P₁/P₂)^γ-1

On substituting the values, we get

(300/T2)1.5 = (3.375/1)^1.5-1

On solving above, we get

T₂ = 200 K

⇒ T₂ = 200 - 273 = -73 ℃

Ques. A gas suddenly compressed to 1/4th of its original volume. What will be the rise in temperature of the gas if the initial temperature is 27 ℃? (γ = 1.5)

Ans. Let

• V₁ be the initial volume of the gas
• V₂ be the final volume of the gas
• T₁ be the initial temperature of the gas
• T₂ be the final temperature of the gas

Given

• The initial temperature of the gas is, T₁ = 27 ℃ = 300 K
• Final volume, V₂ = V₁/4

For adiabatic expression, we have PV^γ = constant

But from ideal gas equation, for one mole of ideal gas, we have PV = RT

⇒ P = RT/V

Therefore adiabatic expression becomes

(RT/V)V^γ = constant

⇒ TV^γ-1 = constant

⇒ T₁V₁^γ-1 = T₂V₂^γ-1

⇒ (T₁/T₂) = (V₂/V₁)^γ-1

On substituting the values, we get

(300/T₂) = [(V₁/4)/V₁)]^1.5-1

On solving above, we get

T₂ = 600 K

⇒ T₂ = 600 - 273 = 327 ℃

Rise in temperature, ΔT = T₂ - T₁ = 327 - 27 = 300 ℃

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