91Ó°ÊÓ

The first law of thermodynamics is like the conservation of energy but applied to thermodynamics. It asserts that energy can neither be created nor destroyed in an isolated system. Instead, it can only be transferred or converted from one form to another.
In the context of a gas in a cylinder, this law can be expressed with the formula:

• \( \Delta U = Q - W \)

Where:

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

This relationship helps us understand how the internal energy changes as heat transfers into or out of a system, and as work is done by or on the system. Using this formula, we can determine the unknowns if we have the right quantities for the other variables.

Work, in thermodynamics, refers to the energy transferred when a force is applied to move an object. For gases, work is often associated with their expansion or compression.
The formula to calculate work done by a gas when it changes volume at constant pressure is:

• \( W = P(V_f - V_i) \)

Where:

• \( P \) is the pressure
• \( V_f \) and \( V_i \) are the final and initial volumes, respectively

In the exercise, the equation provided a negative value for work \( (-1.15 \times 10^5 \, \mathrm{J}) \), indicating that the work was done on the gas (since the gas was compressed) rather than by the gas.

Heat flow refers to the transfer of thermal energy from one object or system to another. In thermodynamics, heat is added or removed as the system does work, or changes temperature or state.
The sign of \( Q \) determines the direction:

• If \( Q \) is positive, heat flows into the system.
• If \( Q \) is negative, heat flows out.

For the given problem, we found \( Q = -2.55 \times 10^5 \, \mathrm{J} \). This negative sign indicates that heat is leaving the gas system. Thus, there was a net heat loss during the compression process, leading to a decrease in internal energy.

Internal energy in a thermodynamic system refers to the total energy stored within the system, including kinetic and potential energies of molecules.
The change in internal energy \( \Delta U \) can be determined through the first law of thermodynamics. Given that \( \Delta U \) was reported as \(-1.40 \times 10^5 \, \mathrm{J} \), it's clear that there was a decrease in internal energy of the gas system.
This decrease can happen when the system performs work on its surroundings (resulting in energy leaving the system) and also when there is a loss of heat, as shown in the initial exercise. This makes sure energy conservation is upheld as dictated by the first law of thermodynamics.