Thermodynamics

Step 1: Understanding the Concept:
The question asks about the thermodynamic nature of the process of sound propagation in a fluid. Sound waves are mechanical waves that travel as a series of compressions and rarefactions.
Step 2: Detailed Explanation:


The compressions and rarefactions of a sound wave occur very rapidly. This rapid nature means there is insufficient time for significant heat exchange to occur between the compressed (slightly hotter) regions and the rarefied (slightly cooler) regions. A process with negligible heat transfer is defined as adiabatic. This eliminates option (A) Isothermally, which was Newton's incorrect initial assumption.
Option (C) Isobarically is incorrect by definition, as a sound wave is fundamentally a pressure wave, meaning pressure varies.
The question specifies a "weak pressure wave". In this context, "weak" implies that the process is nearly reversible, with minimal energy dissipation due to effects like viscosity or thermal conduction.
A process that is both reversible and adiabatic is defined as isentropic (constant entropy).
While the process is adiabatic (Option B), the term isentropic (Option D) is more precise and complete because it also implies reversibility, which is a key assumption in the standard derivation for the speed of sound.

Step 3: Final Answer:
Given the options, "Isentropically" is the most accurate and specific description of the propagation of a weak sound wave.

Step 1: Understanding the Concept:
This question requires matching each of the four fundamental laws of thermodynamics with the primary physical concept it defines or is most closely associated with.
Step 2: Detailed Explanation:


A. First Law of Thermodynamics: This law is a statement of the conservation of energy, applied to thermodynamic systems. It introduces internal energy (U) as a state function, with the relation . Therefore, A matches II.
B. Second Law of Thermodynamics: This law describes the direction of spontaneous processes and the concept of irreversibility. It introduces the state function of entropy (S) to quantify this. Therefore, B matches III.
C. Third Law of Thermodynamics: This law establishes an absolute scale for entropy by stating that the entropy of a perfect crystal approaches zero as the temperature approaches absolute zero. This is also known as the Nernst Theorem. Therefore, C matches IV.
D. Zeroth Law of Thermodynamics: This law states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This law provides the formal definition of temperature as a fundamental property. Therefore, D matches I.

Step 3: Final Answer:
The correct matching is: A-II, B-III, C-IV, D-I.

Step 1: Understanding the Concept:
The molar specific heat at constant volume ( ) of a gas is related to its internal energy, which in turn depends on the number of degrees of freedom of its molecules, according to the equipartition theorem. This question asks for the value of for a diatomic gas.
Step 2: Key Formula or Approach:
According to the equipartition theorem, the average energy per molecule associated with each degree of freedom is , where is the Boltzmann constant and T is the temperature.
The molar internal energy U is given by , where 'f' is the number of degrees of freedom.
The molar specific heat at constant volume is defined as .
Step 3: Detailed Explanation:
For a diatomic molecule (like N or O ) at moderate temperatures, we consider its translational and rotational degrees of freedom:


Translational degrees of freedom: 3 (motion along x, y, and z axes).
Rotational degrees of freedom: 2 (rotation about two axes perpendicular to the bond axis; rotation about the bond axis itself has a negligible moment of inertia).
Vibrational degrees of freedom are typically not excited at room temperature and are ignored unless stated otherwise.
Total degrees of freedom, .
Now, calculate the internal energy per mole:

Finally, calculate :

Step 4: Final Answer:
The value of specific heat at constant volume ( ) for diatomic molecules is .

Step 1: Understanding the Concept:
This question requires an understanding of the scope and limitations of the First and Second Laws of Thermodynamics, specifically concerning the directionality of thermodynamic processes.
Step 2: Detailed Explanation:
Statement A and B: The First Law of Thermodynamics is the law of conservation of energy ( ). It states that energy cannot be created or destroyed. However, it places no restriction on the direction of a process. For example, the First Law would allow heat to flow spontaneously from a cold body to a hot body, as long as energy is conserved. Since this does not happen in reality, we know the First Law does not specify the direction of spontaneous change.
Therefore, statement A is correct and statement B is incorrect.
Statement C and D: The Second Law of Thermodynamics was formulated precisely to address the limitation of the First Law. The Second Law introduces the concept of entropy and states that for any spontaneous process in an isolated system, the total entropy must increase. This provides a clear "arrow of time" or direction for physical processes. A process will only occur spontaneously if it leads to an increase in the total entropy of the universe.
Therefore, statement D is correct and statement C is incorrect.
Step 3: Final Answer:
The correct statements are A and D.

Step 1: Understanding the Concept:
This question tests the definitions of the four basic types of thermodynamic processes.
Step 2: Detailed Explanation:


A. Isothermal process: The prefix "iso-" means "constant" or "equal", and "thermal" refers to temperature. An isothermal process is one that occurs at constant temperature. Therefore, A matches III.
B. Adiabatic Process: An adiabatic process is one in which there is no heat transfer ( ) into or out of the system. Therefore, B matches IV.
C. Isobaric Process: The prefix "iso-" means "constant", and "baric" refers to pressure (from "bar"). An isobaric process is one that occurs at constant pressure. Therefore, C matches II.
D. Isochoric process: The prefix "iso-" means "constant", and "choric" refers to volume. An isochoric process is one that occurs at constant volume. It is also known as an isometric process. Therefore, D matches I.

Step 3: Final Answer:
The correct matching is: A-III, B-IV, C-II, D-I.

Step 1: Understanding the Concept:
The question asks for the correct statement describing the nature of entropy, which is governed by the Second Law of Thermodynamics.
Step 2: Detailed Explanation:
Let's analyze each statement:
(A) "Entropy is intensive property and entropy of system is sum of entropy of its parts." This is incorrect. Entropy is an extensive property, meaning it scales with the size of the system. The total entropy of a system is indeed the sum of the entropy of its parts, which is the definition of an extensive property.
(B) "Entropy can be produced, or in the limit of a reversible process be conserved, but entropy can never be destroyed." This is a correct statement of the Second Law of Thermodynamics. For any real (irreversible) process, the total entropy of an isolated system (or the universe) increases ( ). In the idealized case of a reversible process, the total entropy is conserved ( ). The law forbids any process in which the total entropy would decrease.
(C) "Entropy is not transferred with heat, but there is entropy transfer associated with energy transfer as work." This is incorrect. Entropy transfer is fundamentally associated with heat transfer ( ). There is no entropy transfer associated with work in a reversible process.
(D) "Entropy can not measures the amount of microscopic randomness." This is incorrect. The statistical definition of entropy, , directly relates entropy to , the number of accessible microstates. Therefore, entropy is precisely the measure of microscopic randomness or disorder.
Step 3: Final Answer:
The only correct statement is (B), which is a qualitative summary of the Second Law of Thermodynamics.

Step 1: Understanding the Concept:
This question relates to the State Postulate of thermodynamics. The State Postulate defines the number of independent properties required to completely fix the state of a simple thermodynamic system. A simple fluid (or a simple compressible system) is one that is not influenced by electrical, magnetic, gravitational, motion, and surface tension effects.
Step 2: Detailed Explanation:
The State Postulate states that the thermodynamic state of a simple fluid is completely specified by two independent, intensive properties.
The given equation of state for an ideal gas, , relates three intensive properties:


P (Pressure)
(Density)
T (Temperature)
(R is the specific gas constant, which is a constant for a particular gas).
This equation shows that these three properties are not independent. If you specify the values of any two of them (for example, T and ), the value of the third property (P) is automatically determined by the equation. Therefore, only two of these properties can be varied independently to define the state of the gas.
Step 3: Final Answer:
For a simple fluid like an ideal gas, there are only two independent intensive thermodynamic properties.

Step 1: Understanding the Concept:
The question asks for the relationship between the specific gas constant (R) and the universal gas constant ( or sometimes ). The ideal gas law can be written in two forms: one using moles and the universal constant, and one using mass and the specific constant.
Step 2: Key Formula or Approach:
The molar form of the ideal gas law is:

where is the number of moles.
The mass-based form of the ideal gas law is:

where is the mass of the gas and R is the specific gas constant.
The number of moles is related to mass and molar mass by:

Step 3: Detailed Explanation:
We can derive the relationship by equating the two forms of the ideal gas law. Substitute into the molar form:

Compare this with the mass-based form, :

By comparing the terms, we can see that:

Step 4: Final Answer:
The specific gas constant R is equal to the universal gas constant divided by the molar mass M.

Step 1: Understanding the Concept:
The Carnot cycle is a theoretical thermodynamic cycle that represents the most efficient possible cycle for converting heat into work or vice versa between two heat reservoirs. It consists of four reversible processes. The question asks for the correct order of these processes for a heat engine.
Step 2: Detailed Explanation:
The standard Carnot heat engine cycle proceeds as follows:
1. Reversible Isothermal Expansion: The gas expands at a constant high temperature , absorbing heat from the hot reservoir. This corresponds to step A.
2. Reversible Adiabatic Expansion: The gas continues to expand, but now adiabatically (no heat exchange). Its temperature drops from to the low temperature . This corresponds to step D.
3. Reversible Isothermal Compression: The gas is compressed at a constant low temperature , rejecting heat to the cold reservoir. This corresponds to step B.
4. Reversible Adiabatic Compression: The gas is further compressed adiabatically, causing its temperature to rise from back to the initial high temperature , completing the cycle. This corresponds to step C.
Step 3: Final Answer:
The correct sequence of operations for a Carnot cycle is Isothermal Expansion Adiabatic Expansion Isothermal Compression Adiabatic Compression. This corresponds to the sequence A, D, B, C.