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Degree of Freedom
The degree of freedom for a dynamic system is the number of directions in which it can move freely or the number of coordinates required to describe completely the position and configuration of the system.
It is denoted by for N.
Degree of freedom of a system is given by
f or N = 3A – R
where A = number of particles in the system and R = number of independent relations.
Degree of Freedom
- For monatomic gas = 3
- For diatomic gas = 5
- For non-linear triatomic gas = 6
- For linear triatomic gas = 7
Specific heat of a gas
(a) At constant volume, CV = f/2 R
(b) At constant pressure, cp = (f/2 + 1)R
(c) Ratio of specific heats of a gas at constant pressure and at constant volume is given by
γ = 1 + 2/f
Mean Free Path
The average distance travelled by a molecule between two successive collisions is called mean free path (γ).
Mean free path is given by
γ = kT / √2 π σ2p
where σ = diameter of the molecule, p = pressure of the gas,
T = temperature and k = Botlzmann’s constant.
Mean free path
λ ∝ T and λ ∝ 1/p
Brownian Motion
The continuous random motion of the particles of microscopic size suspended in air or any liquid, is called Brownian of microscopic motion.
Brownian suspended motion in both is observed with many liquids and gases.
Brownian motion is due to the unequal bombardment of the suspended Particles by the molecules of the surrounding medium.
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FAQs on Degree of Freedom, Specific Heat Capacity & Mean Free Path - Physics for JEE Main & Advanced
| 1. What is the concept of degrees of freedom in thermodynamics? |  |
Ans. In thermodynamics, the concept of degrees of freedom refers to the number of independent variables or parameters that can be varied to describe the system's state. It represents the number of ways in which the system can store or distribute energy. For example, a gas molecule in a three-dimensional space has three degrees of freedom associated with its translational motion.
| 2. How does specific heat capacity affect the heating of a substance? | |
Ans. Specific heat capacity is the amount of heat energy required to raise the temperature of a substance by a certain amount. It determines how much heat energy a substance can absorb or release without undergoing a significant change in temperature. Higher specific heat capacity means that more heat energy is required to raise the temperature of the substance, while lower specific heat capacity implies that less heat energy is needed for the same temperature change.
| 3. What is the significance of mean free path in gas molecules? | |
Ans. The mean free path is the average distance traveled by gas molecules between collisions with each other. It is a measure of how far a gas molecule can move before it encounters another molecule. The mean free path is significant because it determines the behavior of gases under different conditions. For example, in a gas with a long mean free path, the molecules can travel longer distances before colliding, resulting in a lower collision frequency and reduced heat transfer.
| 4. How does the number of degrees of freedom affect the specific heat capacity of a gas molecule? | |
Ans. The number of degrees of freedom of a gas molecule determines its ability to store and transfer energy. According to the equipartition theorem, each degree of freedom contributes equally to the total energy of the molecule. As a result, the greater the number of degrees of freedom, the higher the specific heat capacity of the gas molecule. This is because more degrees of freedom allow the molecule to store more energy in different forms, such as translational, rotational, and vibrational energy.
| 5. How does mean free path affect the thermal conductivity of a gas? | |
Ans. The mean free path of gas molecules is inversely related to the collision frequency and directly affects the thermal conductivity of the gas. A longer mean free path implies that gas molecules can travel longer distances before colliding with each other. This results in reduced collisions and slower heat transfer, leading to lower thermal conductivity. On the other hand, a shorter mean free path increases the collision frequency and enhances heat transfer, resulting in higher thermal conductivity.
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