A gas is enclosed in a container fitted with a piston of cross-sectional area of 0.10 m2. The pressure of the gas is maintained at 8000 N/m2. When heat is slowly transferred, the piston is pushed up through a distance of 4.0 cm. If 42 J heat is transferred to the system during the expansion, what is the change in the internal energy of the system?
Correct answer: B. 10 J
- A. 5 J
- B. 10 J
- C. 20 J
- D. 30 J
- E. 40 J
Explanation
To determine the change in internal energy, apply the first law of thermodynamics: ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.First, calculate the work done by the gas as it pushes the piston: W = P×A×d, where P = 8000 N/m², A = 0.10 m², and d = 0.04 m (converted from cm to m). This gives: W = 8000 × 0.10 × 0.04 = 32 J.Substitute into the first law: ΔU = 42 J - 32 J = 10 J. Thus, the change in internal energy is 10 J.Options A, C, D, and E are incorrect as they result from miscalculations or incorrect assumptions about the heat transferred or work done during the process.
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About First Law of Thermodynamics
The first law relates heat supplied, work done and the change in internal energy through energy conservation. Problems use sign conventions and apply the law to isothermal, adiabatic, isobaric and isochoric processes. Internal energy is a state function, while heat and work depend on the path followed.
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