Thermodynamics

To solve the problem, we need to calculate the net work done by a gas using the area enclosed in the pressure-volume (p-V) curve.

1. Understanding the Problem:
The net work done by a gas is given by the area enclosed in the - curve. In this case, we need to calculate the area of triangle .

2. Formula for the Area of a Triangle:
The formula for the area of a triangle is:

3. Given Values:
- Base of the triangle:
- Height of the triangle:

4. Calculate the Net Work Done:
Substitute the given values into the area formula:

5. Simplify the Expression:
First, multiply the constants:

6. Final Answer:
The net work done by the gas is .

Solution:

We need to analyze the given problem using the first law of thermodynamics, which states:

Where:

• is the change in internal energy.
• is the heat absorbed.
• is the work done by the system.

In a p-V diagram, the work done by the system is represented by the area under the process curve between two states. While it is not described explicitly, we conclude the relative sizes of these areas based on the options provided and likely paths implied by the diagram.

Points to consider:

1. The final states are identical across all processes.
2. According to the first law, if the initial and final states are the same, will be the same for all paths, i.e., .
3. Heat absorbed, , depends on the path taken and will vary with the work done.

Given these observations, to determine the relationships among and , observe that:

1. If the work done is different (which would be inferred from path differences), must differ to keep constant.
2. The process with the largest work done has the highest heat , as remains constant.

Based on the correct answer provided, we have:

• Since the same initial and final states ensure equal changes in internal energy:

This solution coherent with thermodynamic consistency provided the paths are assessed correctly regarding work done (area under the curves). Hence, the correct answer is indeed and .

The energy converted into heat is due to the potential energy of the ice block as it falls.
The potential energy is given by the formula: Where:
- (mass of the ice block),
- (acceleration due to gravity),
- (height).
So, This energy is partially converted to heat. Since 60% of the energy is converted into heat, the heat energy is: Now, to convert this energy into heat, we use the specific heat capacity and the latent heat of fusion.
The amount of ice melted is given by the relation: Where: - (latent heat of fusion), - . So, Thus, the amount of ice melted is .

The amount of heat needed to raise the temperature of a gas is given by the formula: Where:
- is the number of moles of the gas,
- is the molar heat capacity at constant volume,
- is the change in temperature.
Given: - The gas is hydrogen, so , - The cylinder's capacity is , and at STP, 1 mole of gas occupies 22.4 L, so: - The temperature change is . Now, substitute the values:
Thus, the amount of heat needed is 831 J.

Latent heat of vaporization of water (L) = 2240 J/g
Mass of water vaporized (m) = 1 g
Work done in the process of vaporization (W) = 168 J

We need to find the increase in internal energy (ΔU).

The heat supplied to vaporize 1 g of water is given by the latent heat of vaporization.
Heat supplied (Q) = m × L
Q = 1 g × 2240 J/g
Q = 2240 J

According to the first law of thermodynamics, the heat supplied to a system is used to increase its internal energy and to do work on the surroundings.
The first law of thermodynamics equation is:
Q = ΔU + W

Where:
Q is the heat supplied to the system
ΔU is the increase in internal energy of the system
W is the work done by the system

We are given Q = 2240 J and W = 168 J. We need to find ΔU.
Rearranging the equation to solve for ΔU:
ΔU = Q - W

Substitute the given values:
ΔU = 2240 J - 168 J
ΔU = 2072 J

Therefore, the increase in internal energy is 2072 J.

Final Answer: The final answer is 2072 J