91Ó°ÊÓ

The first law of thermodynamics is a fundamental principle that relates the change in internal energy of a system to heat exchange and work done. Simply put, it states that energy can neither be created nor destroyed, only transformed. This law can be expressed with the equation: \( \Delta U = Q + W \).
This equation breaks down the components involved when energy changes occur within a system:

• \( \Delta U \) represents the change in internal energy.
• \( Q \) is the heat added to the system. It's positive if heat is absorbed and negative if it's lost.
• \( W \) is the work done on or by the system. Work done by the system is negative in compression, while it's positive when expansion occurs.

In the context of the given exercise, heat loss is stated as \(-210 \text{ J}\) and the work done during compression is \(-150 \text{ J}\). This ultimately leads to the change in internal energy being \(-360 \text{ J}\), indicating how the system's energy has decreased due to these exchanges. Understanding this helps students grasp how energy conversion works and is a vital principle in many thermodynamic processes.

Internal energy refers to the total energy contained within a substance due to molecular movement and molecular interactions. It is a key concept in thermodynamics, encapsulating both kinetic and potential energy within molecules.
In an ideal gas, molecules move freely without interactions that hold or repulse each other, meaning that their internal energy purely depends on the temperature. Consequently, any changes to the internal energy for an ideal gas are directly linked to temperature changes.
Consider this scenario where heat is lost and work is performed in compression. The internal energy decreases as a result of heat loss \((-210 \text{ J})\) and work done \((-150 \text{ J})\), leading to a total change of \( -360 \text{ J} \). While this may seem simple, it showcases that energy transitions affect molecular motion, thus influencing internal energy.

The ideal gas law is a key equation that links the four properties of gases: pressure, volume, temperature, and the number of moles. It is presented as \( PV = nRT \), where:

• \(P\) is the pressure of the gas.
• \(V\) is the volume.
• \(n\) is the number of moles.
• \(R\) is the ideal gas constant.
• \(T\) is the temperature in Kelvin.

In practice, this law is engaged for calculations when you know three of the four variables, and you aim to solve for the fourth. In the exercise, gas compresses from an initial volume to a smaller one, while pressure remains constant. Hence, using the proportionality \( \frac{T_i}{V_i} = \frac{T_f}{V_f} \) helped find the final temperature, showing the effect on temperature as volume shrinks. From here, one can see how interconnected these properties are in defining the state of an ideal gas.