A gas sample in a piston axsembly expands, doing \(235 \mathrm{~kJ}\) of work on its surroundings at the same time that \(695 \mathrm{~kJ}\) of heat is added to the gas. (a) What is the change in internal encrgy of the gas churing this process? (b) Will the pressure of the gas be higher or lower when these changes are completed?

The change in internal energy is a cornerstone concept in understanding thermodynamic systems. It represents the difference in the amount of energy stored within a system at two different states. During a process like gas expansion in a piston, this change is the result of two main factors: heat transfer to the system and the work done by the system on its surroundings.

When a gas undergoes such a process, its internal energy can increase or decrease. As in our example, if the gas receives more heat (\(695 \text{kJ}\)) than the work it performs (\(235 \text{kJ}\)), its internal energy increases by the difference (\(460 \text{kJ}\)). This increase can lead to a rise in temperature, potentially increase pressure or cause the gas to expand if it's not constrained by its surroundings. Understanding this balance is essential for various applications, from engine efficiency to refrigeration cycles.

Heat transfer is a fundamental process in thermodynamics, referring to the movement of thermal energy from one place to another. It occurs in three primary ways: conduction, convection, and radiation. In the context of our gas expansion example, heat is transferred into the gas, increasing the gas's thermal energy.

Adding heat (\(695 \text{kJ}\)) to a system can result in temperature changes or other forms of energy transformation, such as the work required to expand against external pressure. The ability to quantify this heat transfer is critical for predicting the behavior of the system and understanding how energy is conserved within it, as dictated by the First Law of Thermodynamics.

Work in thermodynamics is defined as the energy transferred when a force acts upon an object over a distance. For a gas within a piston, work is done when the gas expands and pushes the piston, exerting a force over a certain distance. This process is crucial because it represents a form of energy transfer out of the system.

In our scenario, the gas does work amounting to \(235 \text{kJ}\) on the surroundings. It's important to note that work done by the system is considered positive from the surroundings' perspective and negative from the system's perspective, leading to a decrease in the system's internal energy when calculating according to the convention of the First Law of Thermodynamics.

Gas expansion occurs when a gas increases in volume, and it’s a central concept in understanding processes like the one involving our gas sample in a piston assembly. Expansion can be the result of heat transfer to the gas or a reduction in external pressure. It's often accompanied by work done by the gas as it pushes against its confines.

As the gas expands, factors like temperature, pressure, and volume interplay in complex ways that are described by the gas laws. In the given example, although the internal energy increases, which could suggest a pressure increase, the gas expanding can actually reduce pressure if the volume change is significant enough. This nuanced understanding of gas expansion is vital for fields such as engineering and meteorology, where predicting gas behavior under changing conditions is crucial.