91Ó°ÊÓ

The first law of thermodynamics is a fundamental principle central to understanding energy changes in a system. It states that energy cannot be created or destroyed, only converted from one form to another. Simply put, the total energy of an isolated system remains constant. When you look at an isolated system, the increase in internal energy \( \Delta U \) is equivalent to the heat \( Q \) added to the system minus the work \( W \) done by the system. This is captured in the equation: \[ \Delta U = Q - W \]In practical terms, when heat is added to the gas in our exercise, not all the energy increases the system's internal energy. Some of it is used to do work, like moving the piston. Thus, this law helps to determine how much energy really contributes to changing the system's internal condition versus how much energy is spent moving parts, such as pistons. Understanding this balance is key to predicting how systems behave when heat is involved.

Internal energy is the sum of all the kinetic and potential energies of the molecules within a system. It is an intrinsic property and reflects the state of the system due to its temperature, pressure, and volume.
The problem statement mentions an increase in internal energy of \(1730 \text{ J}\) when the gas receives \(2050 \text{ J}\) of heat. This indicates that not all energy added becomes internal energy.
Using the first law of thermodynamics, we see the rest is used for work done by the gas.

• Increases in internal energy can raise the temperature of the gas.
• Higher internal energy can lead to phase changes if enough is accumulated.
• Changes in the internal energy affect how the gas behaves under different conditions.

Visualizing internal energy as a balance book helps you see how adding or removing heat affects what remains in the 'account' as internal energy or what is 'spent' moving objects or increasing volume.

Work done by a gas is the energy transferred when a force moves something. In our exercise, the gas performs work when it pushes the piston up. Even though the piston was initially stationary, the energy from the heated gas allows it to lift it. The work done by the gas can be expressed as: \[ W = F \cdot s \]Where \( W \) is the work, \( F \) is the force exerted by the gas, and \( s \) is the distance through which the force acts.
In solving the exercise, you calculate the work done as \(320 \text{ J}\), the force due to the piston's weight is \(1323 \text{ N}\), and therefore the distance the piston rises is calculated using these values: \[ s = \frac{320\text{ J}}{1323\text{ N}} \approx 0.242 \text{ m} \]Think of it this way: if the gas was able to bump the piston higher, it means more of the heat energy was doing work against gravity, rather than just heating up the gas. The work done by the gas tells us how effectively the energy is being converted to useful mechanical work.