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Air is contained in a vertical piston–cylinder assembly by a piston of mass 50 kg and having a face area of 0.01 m² . The mass of the air is 4 g, and initially the air occupies a volume of 5 liters. The atmosphere exerts a pressure of 100 kPa on the top of the piston. Heat transfer of magnitude 1.41 kJ occurs slowly from the air to the surroundings, and the volume of the air decreases to 0.0025 m³ . Neglecting friction between the piston and the cylinder wall, determine the change in specific internal energy of the air, in kJ/kg.

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Final answer:

To find the change in specific internal energy of the air, calculate the work done during compression using the initial and final volumes, and the constant pressure exerted by the piston and the atmosphere. Apply the first law of thermodynamics to find the change in internal energy, and divide by the mass of the air to determine the specific internal energy change.

Step-by-step explanation:

The question asks to determine the change in specific internal energy of the air in a piston-cylinder assembly after a heat transfer of 1.41 kJ and a volume change.

Firstly, the initial pressure exerted by the piston can be calculated using the formula: P = (m · g + P_{atm} · A) / A, where m is the mass of the piston, g is the acceleration due to gravity, P_{atm} is the atmospheric pressure, and A is the area of the piston face. The pressure remains constant since the piston is mass-loaded and frictionless.

The work done on the air during the compression can be calculated by W = P · ΔV, where ΔV is the change in volume.

The change in internal energy (U) of the gas is given by the first law of thermodynamics, ΔU = Q - W. The specific internal energy change (Δu) is the change in internal energy per unit mass, which is ΔU divided by the mass of the air.

The mass of the air should be in kilograms to match the units of heat transfer (kJ), and the volume in cubic meters to match the standardized SI units. Finally, to find Δu in kJ/kg, simply divide the total internal energy change by the mass of the air in kilograms.

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