Summary of HC Verma Solutions Part 2 Chapter 27: Specific Heat Capacities of Gases
FAQs on HC Verma Solutions Class 12 Chapter 27 - Specific Heat Capacities of Gases
1. Where can I find reliable, step-by-step solutions for HC Verma's 'Concepts of Physics Part 2', Chapter 27?
Vedantu provides comprehensive, expert-verified solutions for HC Verma's Class 12, Chapter 27 - Specific Heat Capacities of Gases. These solutions are crafted to explain each step clearly, focusing on the application of core principles to help students master the numerical problems presented in the textbook.
2. What are the main topics I need to master from HC Verma Chapter 27 for my exams?
Chapter 27 primarily focuses on the thermal properties of gases. Key topics include:
Molar specific heat at constant volume (Cv) and constant pressure (Cp).
The relationship between them, known as Mayer's relation (Cp - Cv = R).
The role of degrees of freedom in determining specific heat for monoatomic, diatomic, and polyatomic gases.
The ratio of specific heats, gamma (γ = Cp/Cv), and its importance in thermodynamic processes.
3. What is the physical significance behind Cp being greater than Cv in gases?
The specific heat at constant pressure (Cp) is always greater than the specific heat at constant volume (Cv). This is because when heat is supplied at constant volume, all the energy goes into increasing the internal energy (and thus temperature) of the gas. However, when heat is supplied at constant pressure, the gas expands. The supplied energy must not only increase the internal energy but also do external work during expansion. Therefore, more heat is required to achieve the same temperature rise at constant pressure.
4. How are 'degrees of freedom' used to solve problems in HC Verma Chapter 27?
Degrees of freedom represent the number of independent ways a gas molecule can store energy. According to the law of equipartition of energy, each degree of freedom contributes (1/2)kT of energy per molecule. In HC Verma problems, you first identify the type of gas:
Monoatomic (e.g., He, Ar): 3 translational degrees of freedom.
Diatomic (e.g., O₂, N₂) at moderate temperatures: 3 translational + 2 rotational = 5 degrees of freedom.
This directly helps calculate the internal energy (U) and subsequently the molar specific heat at constant volume (Cv = (f/2)R), where 'f' is the number of degrees of freedom.
5. How is Mayer's relation (Cp - Cv = R) applied in the solutions for this chapter?
Mayer's relation is a fundamental tool used throughout the solutions for Chapter 27. Once the molar specific heat at constant volume (Cv) is calculated using the degrees of freedom (f), Mayer's relation provides a direct way to find the molar specific heat at constant pressure (Cp). For one mole of an ideal gas, you simply use the formula Cp = Cv + R, where R is the universal gas constant. This is crucial for solving problems involving work done or heat supplied at constant pressure.
6. What is a common error students make when calculating specific heat for diatomic gases like O₂?
A common mistake is assuming that a diatomic gas always has 5 degrees of freedom. While this is true at moderate temperatures, HC Verma problems sometimes hint at very high temperatures. At such high temperatures, vibrational modes also become active, adding 2 more degrees of freedom (one for kinetic and one for potential energy of vibration). This changes the total degrees of freedom to 7, significantly altering the calculated values of Cv and Cp. Always check the problem's context for temperature conditions.
7. How does the adiabatic exponent (γ) from this chapter apply to thermodynamic processes?
The adiabatic exponent, γ = Cp/Cv, is a critical parameter that defines the behavior of a gas during an adiabatic process (a process with no heat exchange). The equation for such a process is PVγ = constant. The value of γ depends on the atomicity of the gas (e.g., 5/3 for monoatomic, 7/5 for diatomic). Solutions in HC Verma for problems on adiabatic expansion or compression frequently require you to first calculate γ using the concepts from Chapter 27.
8. For JEE Main/Advanced, which question types from HC Verma's Chapter 27 are most important?
For competitive exams like JEE, focus on problems from Chapter 27 involving:
Mixtures of gases: Calculating the equivalent Cp, Cv, and γ for a mixture of two or more non-reacting gases.
Application of the first law of thermodynamics: Questions that combine specific heat concepts with work done (W) and change in internal energy (ΔU).
Processes on P-V diagrams: Identifying the molar heat capacity for a given polytropic process (PVx = constant), which is a common advanced problem type.
