Problem 80 - A Complete Resource Book in Chemistry for JEE Main

Question

The increase in internal energy of the system is 100 when \(300 \mathrm{~J}\) of heat is supplied to it. What is the amount of work done by the system (a) \(-200 \mathrm{~J}\) (b) \(+200 \mathrm{~J}\) (c) \(-300 \mathrm{~J}\) (d) \(-400 \mathrm{~J}\)

Step-by-Step Solution

Answer

The work done by the system is -200 J, which matches option (a).

Step 1: Understand the Question

We are given the increase in internal energy (9 = 100 J) and the heat supplied to the system (9 = 300 J). We need to find the work done (9) by the system.

Step 2: Apply the First Law of Thermodynamics

The first law of thermodynamics is given by 9 = 9. In this equation, 9 represents the change in internal energy, 9 is the heat supplied to the system, and 9 is the work done by the system.

Step 3: Plug in the Values

Using the first law, substitute 9 = 100 J and 9 = 300 J into the equation 9 = 9. This gives us: 100 = 300 + 9.

Step 4: Solve for Work Done

Rearrange the equation 100 = 300 + 9 to find 9. This gives us 9 = 100 - 300 = -200 J.

Step 5: Identify the Correct Option

The calculated work done by the system is 9 = -200 J, which corresponds to option (a).

Key Concepts

Internal Energy

In thermodynamics, internal energy is a crucial concept. It represents the total energy contained within a system. This is the energy associated with the random, disordered motion of molecules and comes in both kinetic and potential forms. Internal energy can change when energy is transferred in or out of the system.
The First Law of Thermodynamics emphasizes that any change in internal energy depends on two factors:

• Heat added to the system
• Work done by the system

When you supply heat to a system, its internal energy tends to increase. This allows the system to either do work on its surroundings or increase its energy reserves. For example, in the problem given, the internal energy increases by 100 J, signifying that the energy stored in the system's molecules increased by that amount.

Heat Transfer

Heat transfer is the process of energy moving from one body or system to another as a result of thermal interactions. It is critical in explaining the behavior of systems under the First Law of Thermodynamics. Heat can enter or leave a system, and this affects the overall energy balance.
Several mechanisms allow thermal energy to be exchanged:

• Conduction: Direct transfer of energy through a medium without movement of the medium itself.
• Convection: Transfer of heat due to the movement of fluid (like air or water).
• Radiation: Transfer of energy through electromagnetic waves.

In the exercise example, when 300 J of heat is supplied to a system, it indicates that 300 joules of energy have been transferred into the system. This process impacts the internal energy, and influences whether the system performs work on its surroundings.

Work Done

Work done by a system relates to energy transfer, typically resulting from motion or forceful interaction. In the context of thermodynamics, work is performed by a system when it causes displacement or a volume change in its environment. A negative work value implies that energy is expended by the system, while a positive value means the system receives work or energy.
According to the First Law of Thermodynamics, \[ \Delta U = Q - W \]where:

• \( \Delta U \) is the change in internal energy
• \( Q \) is the heat added to the system
• \( W \) is the work done by the system

In the provided example, the system's internal energy increase is 100 J while it receives 300 J of heat. Rearranging the formula to solve for work \( W \) yields \( W = 300 - 100 = -200 \text{ J} \). This negative value indicates the system did 200 J of work on its surroundings, extracting that energy from the internal reserve.