A system does \(100 \mathrm{~J}\) work on surroundings by absorbing \(150 \mathrm{~J}\) of heat. Calculate the change in internal energy.

Internal energy can be thought of as the energy contained within a system. It is the sum of potential and kinetic energy of all the particles within the system. This energy can change when heat is exchanged or when work is done on or by the system.

In the given exercise, the internal energy change, denoted by \( \Delta U \), must be calculated to understand the system's behavior after heat absorption and work done. An increase in \( \Delta U \) signifies that the system has gained energy, either through receiving heat (\( Q \) is positive) or by the surroundings doing work on it (when \( W \) is negative). Conversely, a decrease in \( \Delta U \) indicates the system has lost energy.

Heat transfer refers to the movement of thermal energy from one place to another. It's crucial in thermodynamics as it affects the internal energy. There are three modes of heat transfer: conduction, convection, and radiation.

In our exercise, we are focused on the quantity of heat (\( Q \)) transferred into the system, which is positively contributing to the internal energy. It's essential to note that heat transfer is not always positive; when a system loses heat, \( Q \) would be negative. The concept of heat transfer is greatly emphasized in IIT-JEE chemistry because of its implications in various chemical reactions and processes.

The work-energy principle is a fundamental concept that connects work (\( W \)) with changes in kinetic or potential energy, contributing to changes in internal energy within a system. When work is done by the system, as in our exercise, it means energy is being transferred out of the system, resulting in a decrease in internal energy.

Relation to Internal Energy

In this context, mechanical work done by the system on the surroundings decreases its internal energy. This action is represented in the first law of thermodynamics formula, where \( W \) is subtracted from \( Q \) to calculate \( \Delta U \).

Solving thermodynamics problems requires a clear understanding of the various laws and concepts, including the first and second laws of thermodynamics, heat transfer, and the work-energy principle. The ability to identify given quantities and apply the correct formulas is key.

To correctly solve the exercise at hand, we recognize it as a direct application of the first law of thermodynamics. By following a step-by-step approach, students can demystify even the most complex thermodynamics problems, which is a critical skill set for exams such as the IIT-JEE, wherein practical and conceptual questions are prominent.

IIT-JEE chemistry involves a rigorous curriculum, and thermodynamics is a core component of it. The subject demands not only an understanding of theoretical concepts but also the application of these concepts in solving practical and numerical problems.

Exercises similar to the one presented here form the basis of many questions in the IIT-JEE exams, which test a student's ability to apply the first law of thermodynamics. Emphasis is given to not only calculating changes in internal energy, but also comprehending the processes of heat transfer and work associated with chemical reactions and systems.