Piston Pressure: Forces, Physics & Thermodynamics

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Thermodynamics is indeed a branch of physics, and it is commonly included in physics curricula, particularly for engineering students. In analyzing forces on a piston, the primary considerations are the pressures from the gas chambers and any additional forces, such as spring force. The weight of the piston (Fg = mg) is often neglected in certain calculations if the system is assumed to be in equilibrium or if it has a negligible effect on the pressure difference being analyzed. The problem involves calculating the pressure in chamber 1 given specific pressures in chambers 2 and 3, along with the dimensions of the pistons. Understanding these principles is crucial for solving thermodynamic problems effectively.
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So here's an image of a piston. First of all, this is for a thermodynamics class. Is thermodynamics considered to be "physics?" Do physics majors take thermodynamics?

So my question is: When writing the forces on the piston, it is obvious that we have the pressures acting on the piston from the gases in the chambers, and also a spring force on the second piston figure. I thought it was also obvious that there is Fg = mg acting on the piston as well. However, when I peeked at the solution manual, weight is not included in the force equation. Why is this?
 
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The piston diameters in Figure are D1 = 10 cm and D2 = 4 cm. When the pressure in chamber 2 is 2000 kPa and the pressure in chamber 3 is 700 kPa, what is the pressure in chamber 1, in kPa?
 

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