Problem 79 - A Complete Resource Book in Chemistry for JEE Main

Question

The work done by a system is 10 joule, when 40 joule heat is supplied to it. What is the increase in internal energy of system? (a) \(30 \mathrm{~J}\) (b) \(50 \mathrm{~J}\) (c) \(40 \mathrm{~J}\) (d) \(20 \mathrm{~J}\)

Step-by-Step Solution

Answer

The increase in internal energy is 30 J (option a).

Step 1: Understand the Formula

To find the increase in internal energy, we use the first law of thermodynamics: \( \Delta U = Q - W \), where \( \Delta U \) is the change in internal energy, \( Q \) is the heat supplied to the system, and \( W \) is the work done by the system.

Step 2: Plug in the Known Values

From the problem, we know that \( Q = 40 \text{ J} \) and \( W = 10 \text{ J} \). Substitute these values into the formula: \( \Delta U = 40 \text{ J} - 10 \text{ J} \).

Step 3: Perform the Calculation

Calculate \( \Delta U \) by performing the subtraction: \( \Delta U = 40 \text{ J} - 10 \text{ J} = 30 \text{ J} \).

Step 4: Choose the Correct Option

Based on the calculation \( \Delta U = 30 \mathrm{~J} \), the correct answer is option (a).

Key Concepts

Work Done by a System

In the context of the first law of thermodynamics, the term "work done by a system" refers to the energy used by the system to perform tasks. This could include anything from moving pistons in an engine to expanding gases in a container. Work is a form of energy transfer, and it is measured in joules.
To think of it simply, if a system does work, it uses up some of the energy supplied to it. In our exercise, the system does 10 joules of work. This is energy that has left the system, slightly lowering the internal energy balance.
Key concepts to remember about work done by a system:

• Work is always considered as output (energy leaving the system).
• Measured in joules (J).
• Affects the internal energy balance of the system since energy is spent.

Heat Supplied

When we talk about heat supplied, we're referring to the energy transferred to a system to increase its energy content. Heat, like work, is a form of energy transfer, and is also measured in joules.
In our scenario, the system receives 40 joules of heat. This energy input contributes to raising the internal energy of the system.
The important things to know about heat supplied:

• It is energy added to a system, increasing its potential to do work.
• Measured in joules (J) like work.
• Plays a major role in determining the change in a system's internal energy.

Internal Energy Change

The concept of internal energy change is central to understanding thermodynamic processes. Internal energy (8 U9) is the total energy contained within a system, which includes both kinetic and potential energy at the molecular level.
The first law of thermodynamics helps us calculate this change: 8 U = Q - W. Here, 8 U stands for the change in internal energy, Q for the heat supplied, and W for the work done by the system.
Using our example, we plug in the values given: 8 U = 40 J (for heat supplied) - 10 J (for work done).
This calculation shows that the internal energy change is 30 J, meaning the system's internal energy has increased by 30 joules due to the heat received and work performed.

• The change in internal energy depends on both heat added and work done accordingly.
• Results in volumetric or temperature changes of the system.
• A positive change indicates the system has gained energy, while a negative change shows a loss in energy.