The pressure in an ideal gas is slowly reduced to 14^(1)/(4) its initial value, while being kept

step 1 Now in this question we are given that the pressure in an idle gas is slowly reduced to 141 over

The pressure in an ideal gas is slowly reduced to 14^(1)/(4)...

The pressure in an ideal gas is slowly reduced to $14^{\frac{1}{4}}$ its initial value, while being kept in a container with rigid walls. In the process $800 \mathrm{~kJ}$ of heat leaves the gas. What is the change in internal energy of the gas during this process?

Key Concepts

Ideal Gas

An ideal gas is a theoretical gas composed of a large number of identical particles moving in random directions, where the particles interact only through elastic collisions. Its behavior is described by the ideal gas law, which relates pressure, volume, and temperature. This concept is essential for understanding problems involving state changes and energy variations, as it allows one to use specific relationships between thermodynamic quantities without considering intermolecular forces.

Internal Energy

The internal energy of a system refers to the total energy contained within the system, stemming from both the kinetic and potential energies of its molecules. In an ideal gas, the internal energy is solely a function of temperature, meaning any change in the gas’s temperature directly leads to a change in its internal energy. This relation is key in analyzing energy exchanges during thermodynamic processes.

First Law of Thermodynamics

The First Law of Thermodynamics is a statement of energy conservation, expressing that the change in internal energy of a system is equal to the heat added to the system plus the work done on the system. This principle forms the cornerstone for solving many thermodynamic problems by linking heat, work, and internal energy changes.

Isochoric Process

An isochoric process is one that occurs at a constant volume, meaning that the system’s volume remains fixed throughout the process. In such scenarios, no work is done by or on the system because work in thermodynamics is typically associated with volume change. This simplification is crucial for problem-solving as it directly bounds the energy changes to heat transfer and changes in internal energy only.

Transcript

Please give Ace some feedback