A piston/cylinder has 1.5 kg of air at 300 K and 150 kPa . It is now heated up in a two step pro

step 1 Here the two processes are we have, first one to two processes are constant volume. First is con

A piston/cylinder has 1.5 kg of air at 300 K and 150 kPa ....

A piston/cylinder has $1.5 \mathrm{kg}$ of air at $300 \mathrm{K}$ and 150 $\mathrm{kPa} .$ It is now heated up in a two step process. First constant volume to $1000 \mathrm{K}$ (state 2 ) then followed by a constant pressure process to $1500 \mathrm{K}$, state 3 . Find the final volume and the work in the process.

Key Concepts

Ideal Gas Law

The Ideal Gas Law (pV = mRT) relates pressure, volume, temperature, and mass of an ideal gas using the specific gas constant. It serves as the foundation for analyzing state changes in gases, allowing one to compute unknown properties when the others are known. This law is crucial for transitioning between different states in thermodynamic processes.

Constant Volume Process

In a constant volume (isochoric) process, the volume of the gas remains unchanged while other properties such as temperature and pressure vary. Since the volume is fixed, no boundary work is done by or on the system. This concept simplifies the analysis of energy transfer during heating or cooling when volume is kept constant.

Constant Pressure Process

A constant pressure (isobaric) process is characterized by the pressure staying fixed while the volume and temperature of the gas may change. This type of process is common in piston-cylinder systems where the piston moves to allow expansion or compression at a steady pressure. It plays a key role in calculating work done, as work is directly related to volume change while the pressure is constant.

Thermodynamic Work

Work in thermodynamic processes, particularly for gases, is generally defined as the energy transferred by the system during expansion or compression. For constant pressure processes, work is calculated as the product of the constant pressure and the change in volume. Understanding this concept is essential for analyzing energy interactions in multi-step thermodynamic problems.

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