A system releases 511 kJ of heat and does 125 kJ of work on the surroundings. What is the change in internal energy of the system?

Verified step by step guidance

1. Identify the formula for the change in internal energy: \( \Delta U = q + w \), where \( q \) is the heat exchanged and \( w \) is the work done.
2. Determine the sign of \( q \). Since the system releases heat, \( q = -511 \text{ kJ} \).
3. Determine the sign of \( w \). Since the system does work on the surroundings, \( w = -125 \text{ kJ} \).
4. Substitute the values of \( q \) and \( w \) into the formula: \( \Delta U = -511 \text{ kJ} + (-125 \text{ kJ}) \).
5. Calculate \( \Delta U \) by adding the values: \( \Delta U = -511 \text{ kJ} - 125 \text{ kJ} \).

Key Concepts

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. It establishes the relationship between the internal energy of a system, heat exchanged, and work done. Mathematically, it is expressed as ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.

Internal Energy

Internal energy is the total energy contained within a system, encompassing kinetic and potential energies of the particles. It is a state function, meaning it depends only on the current state of the system, not on how it reached that state. Changes in internal energy are crucial for understanding thermodynamic processes and energy transfers.

Heat and Work

In thermodynamics, heat refers to the energy transferred due to temperature differences, while work is the energy transferred when a force is applied over a distance. Both heat and work are forms of energy transfer that can affect a system's internal energy. Understanding how these two forms of energy interact is essential for applying the First Law of Thermodynamics.