Thermal Physics

Concept: Since the piston moves slowly, the process is isobaric (pressure constant). Heat supplied: For a diatomic gas with only rotational modes:
Step 1:Find molar heat capacity at constant pressure.
Step 2:Calculate heat supplied.

Step 1: Understanding the Concept:
This problem involves the principle of calorimetry where heat lost by one substance equals heat gained by another. One part of the water loses sensible heat during cooling. The other part gains sensible heat to reach boiling point and then gains latent heat to evaporate.
Step 2: Detailed Explanation:
Let and .
Heat Lost by grams of water:
Cooling from to :
.
Heat Gained by grams of water:
1. Heating from to :
.
2. Evaporation at :
.
Total heat gained:
.
Equating heat lost and heat gained:


.
Step 3: Final Answer:
The value of to the closest integer is 922.

Step 1: Understanding the Concept:
The average kinetic energy of a gas molecule depends solely on its absolute temperature. However, the root mean square velocity ( ) depends on both the temperature and the molar mass of the gas.

Step 2: Key Formula or Approach:
1. Average Kinetic Energy ( ) = .
2. Root Mean Square Velocity ( ) = .

Step 3: Detailed Explanation:
- Statement-1: Since , if two gases have the same average kinetic energy, they must be at the same temperature . This statement is true.
- Statement-2: At the same temperature, . Since the molar mass of (2 g/mol) is much smaller than that of (32 g/mol), will have a much higher than . This statement is false.

Step 4: Final Answer:
Statement-1 is true and Statement-2 is false.

Step 1: Understanding the Concept:
This is a relative motion problem. The velocity of the stone in the ground frame must be calculated first, and then its relative velocity with respect to car A is determined.

Step 2: Key Formula or Approach:
1. Velocity of stone w.r.t ground: . 2. Velocity of stone w.r.t car A: .

Step 3: Detailed Explanation:
Given: km/hr, km/hr, . Relative velocity of stone w.r.t A in km/hr: Convert 5 m/s to km/hr: km/hr. We know km/hr:

Step 4: Final Answer:
The value of is 38 km/hr.

Concept: Heat transfer involves: • Sensible heat: • Latent heat: Given: • Specific heat of water • Latent heat of vaporisation
Step 1: Heat released when gm cools from to .
Step 2: Heat required to convert gm water at to steam at . Two steps involved: • Heating from to • Vaporisation at
Step 3: Equate the two heats. Thus,

Step 1: Write the magnification formula.
For a mirror, the magnification is given by: where is the image distance, and is the object distance. Here, .
Step 2: Use the mirror formula.
The mirror formula is given by: where is the focal length.
Step 3: Substitute the magnification and mirror formula.
From the magnification equation, we have: Substitute into the mirror formula: Simplify the equation:
Step 4: Solve for .
Solving the above equation, we get:
Step 5: Find the two positions.
For , we have: Now, use the mirror equation for the second position where the magnification is . From the mirror formula, the distance between the two positions is:

Let the masses of both particles be , and their initial velocities be: - - The position vectors of the two particles at any time are given by: Now, the position of the center of mass is given by: Substituting the expressions for and : Thus, the center of mass follows a straight line, because there is no or higher power term. Final Answer: (A) straight line

In Young’s Double Slit Experiment (YDSE), the intensity at a point on the screen is given by: where:
- is the maximum intensity,
- is the path difference,
- is the wavelength of light.
We are given that the intensity is , so: This implies: Thus: Solving for : Substitute the value of : Thus, the path difference at point P is . Final Answer: Option (C) 3000 .

Step 1: Understanding the Concept:
When an object is heated, its expansion is proportional to its *current* length prior to that specific heating phase. So the second expansion ( ) will be slightly larger than the first ( ) because it expands from the already elongated length rather than the original .

Step 2: Key Formula or Approach:
Formula for linear expansion: .

Step 3: Detailed Explanation:
We are given the relations for temperature:

.
So, the temperature increment is exactly in both stages.
Stage 1 (Expansion from to ):
Let initial length be .
Increase in length: .
The new length is .
Stage 2 (Expansion from to ):
The strip expands from the new length under the exact same temperature difference .
Increase in length: .
Substitute the expression for :
.
Rearranging terms:
.
Notice that the term in the first parenthesis is exactly . Substituting this back:
.

Step 4: Final Answer:
The value of is .

Step 1: Statement (1) Zeroth law defines thermal equilibrium and introduces the concept of temperature. Step 2: Statement (2) For isothermal process of an ideal gas: Thus Hence is false. Step 3: Statement (3) First law states It relates heat and work but does not introduce the concept of internal energy. Step 4: Statement (4) Product of intensive and extensive property is extensive. Example: Step 5: Statement (5) Ratio of extensive property and mass becomes intensive. Thus statement is false. Correct statements are and .

Concept: For an ideal gas, and From these relations, Step 1: Substitute in heat expression Thus the Assertion is true. Step 2: Check the Reason This relation is also correct from kinetic theory, where is degrees of freedom. However, it does not directly explain the assertion derived above. Thus both statements are true but the reason is not the correct explanation.

Step 1: Formula for linear expansion.
The linear expansion of each rod is given by . The total change in length is the sum of the changes in length of each rod.
Step 2: Calculate the change in length.
For rod 1: For rod 2: Thus, the total change in length is . The final length of the combination is: Step 3: Conclusion.
The final length of the combination is , which corresponds to option (3).