The air in an inflated balloon (defined as the system) warms over a toaster and absorbs 142 J of heat. As it expands, it does 46 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 (\( w \)).
2. Express the first law of thermodynamics as an equation: \( \Delta U = q - w \).
3. Convert all units to be consistent. Note that the work done is given in kilojoules (kJ), so convert it to joules (J) by multiplying by 1000: \( 46 \text{ kJ} = 46000 \text{ J} \).
4. Substitute the given values into the equation: \( \Delta U = 142 \text{ J} - 46000 \text{ J} \).
5. Calculate \( \Delta U \) to find the change in internal energy of the system.

Key Concepts

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. 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 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 can be calculated using the First Law of Thermodynamics.

Work and Heat Transfer

In thermodynamics, work refers to energy transfer that occurs when a force is applied over a distance, while heat is the energy transferred due to a temperature difference. Both work and heat are forms of energy transfer that affect the internal energy of a system. Understanding how these two forms of energy interact is crucial for solving thermodynamic problems.