The air in an inflated balloon (defined as the system) warms over a toaster and absorbs 115 J of heat. As it expands, it does 77 kJ of work. What is the change in internal energy for the system?

Verified step by step guidance

1. 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 (\( w \)): \( \Delta U = q - w \).
2. Convert the work done from kilojoules to joules to ensure consistent units. Since 1 kJ = 1000 J, convert 77 kJ to joules.
3. Substitute the given values into the equation: \( q = 115 \text{ J} \) and \( w = 77000 \text{ J} \).
4. Calculate the change in internal energy using the formula: \( \Delta U = 115 \text{ J} - 77000 \text{ J} \).
5. Interpret the result: A negative \( \Delta U \) indicates that the system has lost energy overall, meaning the work done by the system exceeds the heat absorbed.

Key Concepts

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. 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. This principle is fundamental for analyzing energy changes 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 can result from heat transfer and work done on or by the system.

Work in Thermodynamics

In thermodynamics, work refers to the energy transferred when a force is applied over a distance. For a gas, work can be calculated when it expands or compresses against an external pressure. The sign of work is crucial: work done by the system on the surroundings is considered negative, while work done on the system is positive.