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A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure Pi = 105 Pa and volume Vi = 10–3 m3 changes to a final state at Pf = (1/ 32) × 105 Pa and Vf = 8 × 10–3 m3 in an adiabatic quasi-static process, such that P3V5 = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at Pi followed by an isochoric (isovolumetric) process at volume Vf . The amount of heat supplied to the system in the two-step process is approximately
  • a)
    112 J
  • b)
    294 J
  • c)
    588 J
  • d)
    813 J
Correct answer is option 'C'. Can you explain this answer?
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Adiabatic Process:
- Initial state: Pi = 105 Pa, Vi = 10^-3 m3
- Final state: Pf = (1/32) x 10^5 Pa, Vf = 8 x 10^-3 m3
- P3V5 = constant

Two-Step Process:
- Step 1: Isobaric expansion at Pi
- Step 2: Isochoric process at Vf

Calculation:
- For the adiabatic process, P3V5 = constant
- (Pi)(Vi)^1.5 = (Pf)(Vf)^1.5
- (105)(10^-3)^1.5 = ((1/32) x 105)(8 x 10^-3)^1.5
- 0.03225 = 0.03225 (validating the adiabatic process)
- Heat supplied in the two-step process can be calculated by finding the work done in each step and adding them.
- Work done in Step 1 (isobaric process): W1 = PΔV = Pi(Vf - Vi)
- Work done in Step 2 (isochoric process): W2 = 0 (no change in volume)
- Total work done = W1 + W2 = Pi(Vf - Vi)
- Total heat supplied = Total work done = 105(8 x 10^-3 - 10^-3) = 588 J
Therefore, the amount of heat supplied to the system in the two-step process is approximately 588 J, which corresponds to option 'C'.
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A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure Pi = 105 Pa and volume Vi = 10–3 m3 changes to a final state at Pf = (1/ 32) × 105 Pa and Vf = 8 × 10–3 m3 in an adiabatic quasi-static process, such that P3V5 = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at Pi followed by an isochoric (isovolumetric) process at volume Vf . The amount of heat supplied to the system in the two-step process is approximatelya)112 Jb)294 Jc)588 Jd)813 JCorrect answer is option 'C'. Can you explain this answer?
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A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure Pi = 105 Pa and volume Vi = 10–3 m3 changes to a final state at Pf = (1/ 32) × 105 Pa and Vf = 8 × 10–3 m3 in an adiabatic quasi-static process, such that P3V5 = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at Pi followed by an isochoric (isovolumetric) process at volume Vf . The amount of heat supplied to the system in the two-step process is approximatelya)112 Jb)294 Jc)588 Jd)813 JCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure Pi = 105 Pa and volume Vi = 10–3 m3 changes to a final state at Pf = (1/ 32) × 105 Pa and Vf = 8 × 10–3 m3 in an adiabatic quasi-static process, such that P3V5 = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at Pi followed by an isochoric (isovolumetric) process at volume Vf . The amount of heat supplied to the system in the two-step process is approximatelya)112 Jb)294 Jc)588 Jd)813 JCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure Pi = 105 Pa and volume Vi = 10–3 m3 changes to a final state at Pf = (1/ 32) × 105 Pa and Vf = 8 × 10–3 m3 in an adiabatic quasi-static process, such that P3V5 = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at Pi followed by an isochoric (isovolumetric) process at volume Vf . The amount of heat supplied to the system in the two-step process is approximatelya)112 Jb)294 Jc)588 Jd)813 JCorrect answer is option 'C'. Can you explain this answer?.
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