Thermodynamics

Step 1: Work done is area under P-V curve.
Step 2: Isobaric expansion gives maximum area for same volume change.

Step 1: In a p-T diagram, - Vertical line constant temperature (isothermal), - Horizontal line constant pressure (isobaric).
Step 2: On a p-V diagram, - Isothermal processes are hyperbolic curves, - Isobaric processes are horizontal straight lines.
Step 3: Matching the sequence of processes in the given cycle, option (B) correctly represents the same cycle in the p-V diagram.

For all processes, change in internal energy does not change.
It depends only on initial and final states.

In an isochoric process, also known as an isovolumetric process, the volume of a system remains constant. In such a process, the work done is always zero.
Work is defined as the energy transferred to or from a system due to the application of a force over a displacement. In an isochoric process, since there is no change in volume, there is no displacement of the system's boundaries, and therefore no work is done. The force may be applied, but if there is no displacement, the work done is zero.
Mathematically, the work done (W) in a process is given by the equation:

where F is the applied force and dx is the displacement.
Since dx is zero in an isochoric process, the integral becomes zero, resulting in no work done.
It's important to note that although no work is done in an isochoric process, heat can still be exchanged with the surroundings, resulting in changes in the system's internal energy. The internal energy change corresponds to the heat transfer into or out of the system.

From the first law of thermodynamics: Where is the heat supplied and is the work done. Given that and , the change in internal energy is: Thus, the rate at which the internal energy increases is .

This problem involves the concept of thermal equilibrium and the principle of heat exchange.
1. Heat Transfer and Energy Conservation: - When two bodies at different temperatures come into thermal contact, heat flows from the hotter body to the cooler body until both bodies reach the same final temperature. This process is governed by the first law of thermodynamics, which is essentially the law of conservation of energy.
2. The amount of heat transferred is given by: Where: - is the mass of the body, - is the specific heat capacity of the material, - is the change in temperature ( ). 3. Equation Setup: - Let the masses of the two bodies be and , their specific heats be and , and their initial temperatures be and , respectively. - The heat lost by the hotter body equals the heat gained by the cooler body. This can be written as: Where is the final temperature that we need to solve for. 4. Solving for Final Temperature: - Rearranging the equation: 5. This equation shows that the final temperature depends on the masses and specific heat capacities of the bodies involved. Option (1) is incorrect because it assumes the final temperature is just the average of the initial temperatures. Option (3) and (4) are incorrect because they ignore the relationship between mass, specific heat, and energy transfer.
Option (2) is correct.

For an isothermal, reversible expansion of an ideal gas, the product of pressure and volume remains constant: Given and , we have: Solving for : Thus, the final pressure is:

To determine the amount of heat required to raise the temperature of the water, we use the formula for heat transfer: , where:

• is the heat energy (in Joules),
• is the mass of the water (in kg),
• is the specific heat capacity (in J/kg°C),
• is the change in temperature (in °C).

Given:

• ,
• ,
• Initial temperature ,
• Final temperature .

The change in temperature is calculated as .

Substitute the values into the formula: .

Calculate:

• ,
• .

Therefore, the heat required to raise the temperature of 2 kg of water from to is .

In an isobaric process, the first law of thermodynamics states: where: - is the heat supplied, - is the work done by the gas, - is the change in internal energy. Substituting the values: Thus, the change in internal energy is:

Given: Work done by the gas at constant pressure is: But this doesn’t match any options — let's recheck: Actually,