91Ó°ÊÓ

A piston-cylinder assembly is a common apparatus used in thermodynamics exercises. It consists of a cylinder that contains gas and a freely movable piston. This setup is ideal for experiments that involve pressure-volume work and heat transfer.
In our problem, the piston has a mass of 25 kg and a face area of 0.005 m². Understanding how the piston moves and interacts within the cylinder is essential, as it helps in calculating the work done by or on the gas. The atmospheric pressure acts on the top of the piston while the gas pressure works inside the cylinder.
This assembly allows for the examination of how changes in pressure, volume, and temperature affect the system. The piston raises or lowers depending on the forces applied, allowing the gas inside to expand or contract. This setup is crucial for applying the first law of thermodynamics and other principles in thermodynamic processes.

Specific internal energy is a measure of the energy stored in a system per unit mass. It is a property of the material and can change due to heat transfer or work done by or on the system. In our problem, we are asked to find the change in specific internal energy of the air.
Specific internal energy helps us understand how the internal energy of a substance changes with changes in temperature, volume, and pressure. In this exercise, the removal of 1 kJ of energy (by heat transfer) causes a decrease in the internal energy of the air contained within the piston-cylinder assembly.
By applying the first law of thermodynamics and calculating the work done by the gas, we can determine the change in internal energy. Finally, dividing this change by the mass of the air gives us the specific internal energy change, which is crucial in thermodynamic analyses of processes involving energy transfer.

The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed, only transferred or transformed. This principle is key in solving problems involving heat and work interactions.
Mathematically, it is represented as: \[ \text{Change in internal energy} = \text{Heat added to the system} - \text{Work done by the system} \]
In this exercise, a certain amount of heat is removed from the gas, which affects its internal energy. To find the change in internal energy, we have to subtract the work done by the gas from the heat removed.
The energy removed is 1 kJ, and the work done by the gas (calculated from the pressure and change in volume) needs to be accounted for. Through this, we get the net change in the internal energy of the gas, which illustrates how energy conservation governs the changes within the piston-cylinder assembly.

Pressure calculation is a fundamental aspect of solving thermodynamic problems, especially when dealing with gases in a piston-cylinder assembly. Pressure within the system can be due to multiple factors, including atmospheric pressure and the pressure exerted by the piston.
In our problem, the pressure exerted by the piston is calculated using the formula: \[ P_{\text{piston}} = \frac{F}{A} \]
This formula requires us to calculate the force due to the weight of the piston (mass times gravity) and then divide this by the cross-sectional area of the piston. The atmospheric pressure and the pressure exerted by the piston combine to give the total pressure inside the cylinder.
Accurate pressure calculation is crucial as it influences the work done by the gas. Understanding these pressure sources and accurately computing them allows us to apply the first law of thermodynamics correctly and solve for changes in energy and specific internal energy.