91Ó°ÊÓ

The First Law of Thermodynamics is a fundamental concept in physics, forming the foundation of much of thermodynamic study. It states that energy cannot be created or destroyed, only transformed from one form to another. In mathematical terms, this can be expressed as:\[ \Delta U = Q - W \]Where:

• \( \Delta U \) is the change in internal energy of the system
• \( Q \) is the heat added to the system
• \( W \) is the work done by the system

This equation implies that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In the context of our exercise, it helps connect the internal changes within the gas to the external influences, explaining how energy transfers occur within the gas system.

Work done by a gas during a process is crucial to understanding how energy flows in thermodynamic systems. When a gas expands or contracts, it does work either on the surrounding environment or has work done onto it. When a gas at constant pressure changes volume, the work done \( W \) can be calculated as:\[ W = P \times (V_f - V_i) \]Here:

• \( P \) is the constant pressure
• \( V_f \) is the final volume
• \( V_i \) is the initial volume

From the exercise, we see that the gas is compressed, indicated by the change from an initial volume of \( 1.70 \ \text{m}^3 \) to a final volume of \( 1.20 \ \text{m}^3 \). Since the work calculated is negative, \( -1.15 \times 10^5 \ \text{J} \), it tells us that work is being done on the gas, compressing it.

Heat exchange in thermodynamic processes is the transfer of thermal energy between the system and its surroundings. It can occur in two directions: heat can be added to the system or removed from it. The direction of heat flow is essential to understanding how a system's energy changes. If \( Q \) is positive, heat enters the system; if \( Q \) is negative, heat leaves.
In our problem, using the rearranged formula from the first law, we calculate that \( Q = -2.55 \times 10^5 \ \text{J} \). This negative sign indicates heat flows out of the gas. This outcome is consistent with the internal energy decreasing and work being performed on the gas.

Internal energy change, \( \Delta U \), is the cumulative effect of energy transformations within a system. It encompasses the total kinetic and potential energy changes resulting from temperature, volume, and pressure variations.
In our exercise, the internal energy of the gas decreases by \( 1.40 \times 10^5 \ \text{J} \). Despite doing work on the gas (compressing it), the overall energy inside the system diminishes. This loss of energy correlates with heat being transferred from the system, as indicated by the negative internal energy change.
This concept shows how internal energy is a measure of the system's total energy status and its changes provide insights into how energy moves within the system in physical terms.