Thermodynamics

When an ideal diatomic gas is heated at constant pressure, the total heat energy supplied is partly used to increase the internal energy of the gas and partly to do work against the external pressure. The fraction of heat energy that increases the internal energy can be calculated by considering the specific heat capacities.

The relationship for heat supplied at constant pressure is given by: Where: - is the number of moles, - is the specific heat capacity at constant pressure, - is the temperature change. For an ideal diatomic gas, the specific heat capacity at constant pressure is related to the specific heat at constant volume by: For a diatomic gas, (because the degrees of freedom for a diatomic gas are 5), and: The heat energy that increases the internal energy of the gas is the part associated with the change in internal energy, which is given by: The fraction of the total heat energy supplied that increases the internal energy is: Substituting the values for and : Thus, the fraction of heat energy that increases the internal energy of the gas is .

Correct Answer:

Correct Answer: (E)

The process in which there is no flow of heat between the system and surroundings is known as an adiabatic process. In an adiabatic process, the system does not exchange heat with the surroundings, and any change in internal energy is solely due to the work done by or on the system.

Let's look at the options:

• Adiabatic process: This is the correct answer. There is no heat exchange between the system and its surroundings.
• Cyclic process: The system returns to its initial state. Heat flow may occur during the cycle.
• Isobaric process: Occurs at constant pressure. Heat exchange can occur.
• Isochoric process: Occurs at constant volume. No work is done, but heat exchange is possible.
• Isothermal process: Occurs at constant temperature. Heat is exchanged to maintain temperature.

Therefore, the correct answer is the adiabatic process, as it involves no heat exchange.

Correct Answer:

Correct Answer: (D) adiabatic process

We are given two thermally insulated identical vessels A and B, connected through a stopcock. Vessel A contains a gas at STP (Standard Temperature and Pressure), and vessel B is completely evacuated. When the stopcock is suddenly opened, the gas expands into vessel B. We need to analyze what happens to the temperature, pressure, and internal energy of the gas.

In this situation, the key concepts to consider are:

• Thermally Insulated System: No heat is exchanged with the surroundings, so the total energy of the system remains constant.
• Expansion into Vacuum (Free Expansion): The gas expands without doing any work (as vessel B is evacuated) and without heat exchange.

In free expansion of an ideal gas:

• The temperature remains constant.
• The internal energy remains constant, as it depends only on temperature for an ideal gas.
• The pressure decreases, because the gas now occupies a larger volume (both vessels A and B).

Therefore, the internal energy remains the same, but the pressure decreases.

Correct Answer:

Correct Answer: (E) internal energy remains the same

The Clausius statement is a formulation of the Second law of thermodynamics, which states that it is impossible for heat to flow spontaneously from a colder body to a hotter body. This principle implies that heat naturally flows from hot to cold objects, and any process that violates this is impossible. Hence, the correct statement is the Second law of thermodynamics.

The correct option is (C) : second law of thermodynamics

An isochoric process is a thermodynamic process in which the volume of the system remains constant. In this process, no work is done by the system, and all the heat supplied goes into changing the internal energy and temperature of the system. This means that the entire heat supplied contributes to raising the temperature of the system. Hence, the process in which the amount of heat supplied goes fully to change its internal energy and temperature is called an isochoric process.

The correct option is (E) : isochoric process

Given:

• Ideal diatomic gas with non-vibrating molecules (degrees of freedom, )
• Volume compressed by a factor of 32 ( )
• No heat exchange (adiabatic process)
• Initial and final pressures: and

Step 1: Adiabatic Process Relation

For an adiabatic process in an ideal gas:

where . For a diatomic gas with :

Step 2: Solve for Pressure Ratio

Rearrange the adiabatic relation:

Substitute :

Calculate :

Thus:

Conclusion:

The ratio is 1:128.

Answer:

Given conditions:

First Law of Thermodynamics:

For ideal gas:

From ideal gas equation:

Internal energy change:

First Law becomes:

Given parameters:

Efficiency definition:

First Law of Thermodynamics:

Heat rejected calculation:

Alternative verification:

Step 1: Let and be the specific heat capacities of the liquids mixed. Since no heat is lost to the environment, the heat lost by the hotter liquid equals the heat gained by the cooler one.
Step 2: Set up the equation based on heat transfer: .
Step 3: Simplify to find the ratio .
Step 4: Thus, the ratio of their specific heat capacities is (inverse of ).

For an ideal gas, the slopes of the adiabatic and isothermal curves are related to the specific heat capacities and the ratio of specific heats .
The general relationship between the slopes of the adiabatic and isothermal curves is given by: The slope of the adiabatic curve and the slope of the isothermal curve are related through the ratio of specific heats .
From the ideal gas laws and thermodynamic relationships, we know that:
Thus, the correct relationship between the slopes is .

In an isochoric process, the volume of the gas remains constant. Since work done is given by: where is the change in volume, if there is no change in volume ( ), the work done by the gas is zero.
Thus, the correct answer is (C).