II. PROBLEM SOLVING. Solve the following problems. Show your complete solution. Box your final answer. Use the extra sheet of paper for this part of examination. 1. A gas is in a closed container and is heated with \( 10 J \) of energy causing the lid to rise 2 m with a \( 3 N \) force. What is the total change in the energy of the system? Use first law of thermodynamics to answer this.

To determine the total change in the energy of the system using the first law of thermodynamics, we can express it as: \[ \Delta U = Q - W \] Where: - \(\Delta U\) is the change in internal energy, - \(Q\) is the heat added to the system, - \(W\) is the work done by the system. In this scenario, \(Q\) is given as \(10 J\), and we need to calculate the work \(W\) done by the gas when it lifts the lid. The work done can be calculated using the formula: \[ W = F \times d \] Where: - \(F = 3 N\) (force) and - \(d = 2 m\) (distance). Thus, the work done is: \[ W = 3 N \times 2 m = 6 J \] Now, we can substitute the values of \(Q\) and \(W\) into the first law of thermodynamics equation: \[ \Delta U = 10 J - 6 J = 4 J \] So the total change in the energy of the system is: \[ \boxed{4 J} \] --- When it comes to physics problems involving thermodynamics, it's crucial to grasp both the concepts of energy transfer and the symbols used in equations. If you confuse work with heat, your final answers may wind up like a hot air balloon losing altitude! So, double-check your definitions to keep things aloft! Understanding the first law of thermodynamics can take you far in real-world applications, from designing engines to analyzing climate models! Recognizing how energy transfers and transformations occur can lead you to innovative solutions in engineering, environmental science, and even daily energy-saving practices. It's exciting to see how these principles shape our world!