The gas in a piston (defined as the system) warms and absorbs 655 J of heat, while performing 344 J of work on the surroundings. What is the change in internal energy for the system?

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Identify the first law of thermodynamics, which states that the change in internal energy (\( \Delta U \)) of a system is equal to the heat added to the system (\( q \)) minus the work done by the system (\( w \)).

Write the formula: \( \Delta U = q - w \).

Substitute the given values into the formula: \( q = 655 \text{ J} \) and \( w = 344 \text{ J} \).

Calculate \( \Delta U \) using the substituted values: \( \Delta U = 655 \text{ J} - 344 \text{ J} \).

Interpret the result: A positive \( \Delta U \) indicates an increase in internal energy, while a negative \( \Delta U \) indicates a decrease.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. In a closed system, the change in internal energy is equal to the heat added to the system minus the work done by the system on its surroundings. This principle is fundamental for analyzing energy transfers in thermodynamic processes.

Internal Energy

Internal energy is the total energy contained within a system, including kinetic and potential energy at the molecular level. It reflects the energy associated with the temperature, phase, and number of particles in the system. Changes in internal energy are crucial for understanding how systems respond to heat and work interactions.

Work and Heat Transfer

In thermodynamics, work and heat are two primary forms of energy transfer. Work is the energy transferred when a force is applied over a distance, while heat is the energy transferred due to a temperature difference. Understanding how these two forms of energy interact is essential for calculating changes in internal energy and analyzing system behavior.

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