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 \(30 \text{ J}\).

Step 1: Understand the First Law of Thermodynamics

The first law of thermodynamics can be expressed as \( \Delta U = Q - W \), 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: Assign values to variables

From the problem, the heat supplied \( Q = 40 \text{ J} \) and the work done \( W = 10 \text{ J} \). We need to find the change in internal energy \( \Delta U \).

Step 3: Substitute values into the formula

Substitute the known values into the formula: \( \Delta U = Q - W = 40 \text{ J} - 10 \text{ J} \).

Step 4: Calculate the change in internal energy

Perform the calculation: \( \Delta U = 30 \text{ J} \).

Key Concepts

Understanding Internal Energy

Internal energy is a core concept in thermodynamics linked to the energy held within a system. Imagine internal energy as the total vibrational, rotational, and translational kinetic energies of particles within a system, along with potential energies like chemical and intermolecular forces.
Internal energy is vital because it helps in understanding how energy transforms within a system.

In the context of the First Law of Thermodynamics, internal energy may change due to:

• Heat transfer (either absorption or release)
• Work done (like expansion or contraction)

Look at it like a bank account: heat added to the system is like making a deposit, and the work done (like the system performing mechanical functions) is akin to a withdrawal. The change in the account balance equivalent is the change in internal energy.

Exploring Heat Supplied

Heat supplied to a system is essentially the energy transferred due to a difference in temperature. It's an exchange that happens from a warmer region to a cooler one.

The heat supplied, denoted by the symbol \( Q \), can be considered as energy flowing into the system in the form of thermal energy. This allows for changes in the system's temperature, internal energy, or phase.
When heat enters the system, it can either increase or transform the system's energy forms. For example:

• Melting ice to water
• Heating a gas to expand

In our example, 40 joules of heat is supplied to the system, meaning the system is gaining energy that can manifest as increased internal energy or be used to perform work.

Deciphering the Work Done by the System

The concept of work done by the system refers to the energy expended by the system to perform tasks like moving pistons, rotating shafts, or generating electricity.

Work done, represented by \( W \), is the energy transferred from the system to its surroundings. It appears when the system engages in actions requiring energy output.

Work in thermodynamics involves a mechanical alteration or force application by the system, leading to energy transfer away from it. In this exercise, the system performs work equivalent to 10 joules. This means that 10 joules of energy were used by the system to do actions or make changes in the environment.