Thermodynamics And Work Done

To solve this problem, we need to calculate the mass of the bullet that melts upon heating. We are given the following data:

• Initial temperature of the bullet,
• Melting temperature of the bullet,
• Total heat required,
• Specific heat capacity of lead,
• Latent heat of fusion of lead,

The problem involves two main heat processes:

1. Heating the bullet from to .
2. Melting the bullet at .

The total heat required can be divided into two parts:

• Heat required to raise the temperature:
• Heat required to melt the bullet:

The total heat is given by the sum of and :

Substituting the known values:

Simplifying this equation:

Solving for :

Thus, the mass of the bullet is 10 grams.

To solve this matching problem, we need to understand the definitions and principles behind each process listed in List-I and find the corresponding process from List-II.

Explanation:

1. Isothermal Process (III): In this process, the temperature remains constant, meaning the internal energy does not change. According to Boyle's Law, at constant temperature, the pressure of an ideal gas is inversely proportional to its volume ( ). Thus, A matches with III.
2. Isobaric Process (IV): This process occurs at a constant pressure. The heat absorbed by the system does work as well as increases the internal energy. Hence, B matches with IV.
3. Adiabatic Process (I): No heat is exchanged with the surroundings; hence, all the changes are due to internal energy. Therefore, C matches with I.
4. Isochoric Process (II): This process occurs at constant volume, so no work is done on or by the gas. As a result, D matches with II.

Therefore, the correct answer is A–III, B–IV, C–I, D–II.

Given Data:

Initial temperature,
Final volume,
Ratio of specific heats,

Step 1: Relation for adiabatic process

For a sudden (adiabatic) compression,

Step 2: Substitute given values

Step 3: Calculate final temperature

Step 4: Change in temperature

Final Answer:

In this problem, we are dealing with one mole of an ideal diatomic gas. We need to determine the final temperature after expansion, given that the process is adiabatic. This means no heat is transferred into or out of the system. Let's solve this step-by-step using thermodynamics principles.

For an adiabatic process, the relation between the initial and final states can be given by:

where:

• is the pressure
• is the volume
• is the heat capacity ratio (specific heat ratio), for diatomic gases

The transformation rule for temperature during an adiabatic process for an ideal gas is:

where:

• and are the initial and final temperatures, respectively
• and are the initial and final volumes, respectively

Given that the expansion is a doubling of the volume at a constant pressure, we have:

Substituting this into the equations, we have:

Calculate the above expression:

Thus, we have:

Let's assume the initial temperature to be in Kelvin;
Converting from Celsius (assuming a standard initial temperature, like 27°C which is approximately 300 K for an initial context):

Convert the final temperature to Celsius:

The closest option available is , which is the correct answer.

Therefore, upon the adiabatic expansion, the final temperature of the gas is approximately -56°C.