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A certain amount of an ideal gas is initially at a pressure P1 and temperature T1. First, it undergoes a constant pressure process 1-2 such that T2 = 3T1/4. Then, it undergoes a constant volume process 2-3 such that T3 = T1/2. The ratio of the final volume to the initial volume of the ideal gas is
  • a)
    0.25
  • b)
    0.75
  • c)
    1.0
  • d)
    1.5
Correct answer is option 'B'. Can you explain this answer?
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Constant Pressure Process 1-2:
- During this process, the ideal gas undergoes a constant pressure change from state 1 to state 2.
- Using the ideal gas law (PV = nRT), we can determine the ratio of the final temperature T2 to the initial temperature T1.
- Given that T2 = 3T1/4, we can write P1V1/T1 = P2V2/T2.
- Since the pressure is constant, P1V1/T1 = P2V2/T2 simplifies to V2/V1 = T2/T1 = 3/4.

Constant Volume Process 2-3:
- In this process, the ideal gas undergoes a constant volume change from state 2 to state 3.
- Again using the ideal gas law, we can determine the ratio of the final temperature T3 to the initial temperature T1.
- Given that T3 = T1/2, we can write P2V2/T2 = P3V3/T3.
- Since the volume is constant, P2V2/T2 = P3V3/T3 simplifies to P2/P3 = T2/T3 = 3/2.

Final Volume to Initial Volume Ratio:
- Combining the ratios from the two processes, we have V2/V1 = 3/4 and P2/P3 = 3/2.
- Using the ideal gas law, P1V1/T1 = P2V2/T2 = P3V3/T3, we can determine the final volume to initial volume ratio.
- V3/V1 = (P1/P3) * (T3/T1) = (1/3) * (1/2) = 1/6.
- Therefore, the ratio of the final volume to the initial volume of the ideal gas is 1/6, which is equivalent to 0.75 or 75%. Hence, the correct answer is option B.
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A certain amount of an ideal gas is initially at a pressure P1 and temperature T1. First, itundergoes a constant pressure process 1-2 such that T2 = 3T1/4. Then, it undergoes a constantvolume process 2-3 such that T3 = T1/2. The ratio of the final volume to the initial volume ofthe ideal gas isa)0.25b)0.75c)1.0d)1.5Correct answer is option 'B'. Can you explain this answer?
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A certain amount of an ideal gas is initially at a pressure P1 and temperature T1. First, itundergoes a constant pressure process 1-2 such that T2 = 3T1/4. Then, it undergoes a constantvolume process 2-3 such that T3 = T1/2. The ratio of the final volume to the initial volume ofthe ideal gas isa)0.25b)0.75c)1.0d)1.5Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A certain amount of an ideal gas is initially at a pressure P1 and temperature T1. First, itundergoes a constant pressure process 1-2 such that T2 = 3T1/4. Then, it undergoes a constantvolume process 2-3 such that T3 = T1/2. The ratio of the final volume to the initial volume ofthe ideal gas isa)0.25b)0.75c)1.0d)1.5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain amount of an ideal gas is initially at a pressure P1 and temperature T1. First, itundergoes a constant pressure process 1-2 such that T2 = 3T1/4. Then, it undergoes a constantvolume process 2-3 such that T3 = T1/2. The ratio of the final volume to the initial volume ofthe ideal gas isa)0.25b)0.75c)1.0d)1.5Correct answer is option 'B'. Can you explain this answer?.
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