A certain type of actuator is a closed piston-cylinder mechanism in which the force on the...

 

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A certain type of actuator is a closed piston-cylinder mechanism in which the force on the piston due to the gas under pressure in the cylinder is controlled by heating or cooling. The gas in the cylinder has the properties of an ideal gas. At a given impact (heating), the piston moves, and the gas pressure changes as a function of its position according to the dependence: P(x)=P₁V₁(x)-¹ Derive an equation for the process heat input, Q(x), as a function of the piston position, x, the initial pressure, P₁, the initial position, x₁, and the inner radius of the cylinder, 1. A certain type of actuator is a closed piston-cylinder mechanism in which the force on the piston due to the gas under pressure in the cylinder is controlled by heating or cooling. The gas in the cylinder has the properties of an ideal gas. At a given impact (heating), the piston moves, and the gas pressure changes as a function of its position according to the dependence: P(x)=P₁V₁(x)-¹ Derive an equation for the process heat input, Q(x), as a function of the piston position, x, the initial pressure, P₁, the initial position, x₁, and the inner radius of the cylinder, 1.