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A container having 1 mole1 mole of a gas at a temperature 27℃ has a movable piston which maintains at constant pressure in container of 1 atm1 atm. The gas is compressed until temperature becomes 127℃. The work done is
- a)703 J
- b)831.4 J
- c)121 J
- d)2035 J
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A container having 1 mole1 mole of a gas at a temperature 27℃ has a m...
Given:
- Amount of gas (n) = 1 mole
- Initial temperature (T1) = 27℃
- Final temperature (T2) = 127℃
- Pressure (P) = 1 atm
To find:
Work done during compression (W)
Formula:
Work done (W) = PΔV
Explanation:
1. The work done during compression is given by the formula W = PΔV, where P is the pressure and ΔV is the change in volume.
2. According to the ideal gas law, PV = nRT, where R is the ideal gas constant.
3. Since the pressure and amount of gas remain constant, the equation can be rearranged as V/T = constant.
4. Using this equation, we can find the change in volume (ΔV) by taking the ratio of the initial and final temperatures:
ΔV/V = (T2 - T1)/T1
ΔV = V(T2 - T1)/T1
ΔV = (nRT1)(T2 - T1)/T1
5. Substituting the given values:
ΔV = (1 mol)(0.0821 atm/mol·K)(27 + 273)(127 - 27)/(27 + 273)
ΔV = 0.0821 × 300 × 100
ΔV = 2463 J
6. Finally, substituting the values of pressure (P) and ΔV into the formula for work done:
W = PΔV
W = (1 atm)(2463 J)
W ≈ 2463 J
Therefore, the work done during compression is approximately 2463 J, which is closest to option B (831.4 J).
- Amount of gas (n) = 1 mole
- Initial temperature (T1) = 27℃
- Final temperature (T2) = 127℃
- Pressure (P) = 1 atm
To find:
Work done during compression (W)
Formula:
Work done (W) = PΔV
Explanation:
1. The work done during compression is given by the formula W = PΔV, where P is the pressure and ΔV is the change in volume.
2. According to the ideal gas law, PV = nRT, where R is the ideal gas constant.
3. Since the pressure and amount of gas remain constant, the equation can be rearranged as V/T = constant.
4. Using this equation, we can find the change in volume (ΔV) by taking the ratio of the initial and final temperatures:
ΔV/V = (T2 - T1)/T1
ΔV = V(T2 - T1)/T1
ΔV = (nRT1)(T2 - T1)/T1
5. Substituting the given values:
ΔV = (1 mol)(0.0821 atm/mol·K)(27 + 273)(127 - 27)/(27 + 273)
ΔV = 0.0821 × 300 × 100
ΔV = 2463 J
6. Finally, substituting the values of pressure (P) and ΔV into the formula for work done:
W = PΔV
W = (1 atm)(2463 J)
W ≈ 2463 J
Therefore, the work done during compression is approximately 2463 J, which is closest to option B (831.4 J).
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Community Answer
A container having 1 mole1 mole of a gas at a temperature 27℃ has a m...
Work done at constant pressure is
W = p ΔV = nR ΔT
Where p is presure, ∆V the volume change, R the gas constant, ∆T the change in temperature and n the number of moles.
Given, n = 1, T2 = 127℃ = 400K
∴ W = 1 × 8.314 × (400 − 300)
W = 831.4 J
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A container having 1 mole1 mole of a gas at a temperature 27℃ has a movable piston which maintains at constant pressure in container of 1 atm1 atm. The gas is compressed until temperature becomes 127℃. The work done isa)703 Jb)831.4 Jc)121 Jd)2035 JCorrect answer is option 'B'. Can you explain this answer?
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A container having 1 mole1 mole of a gas at a temperature 27℃ has a movable piston which maintains at constant pressure in container of 1 atm1 atm. The gas is compressed until temperature becomes 127℃. The work done isa)703 Jb)831.4 Jc)121 Jd)2035 JCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A container having 1 mole1 mole of a gas at a temperature 27℃ has a movable piston which maintains at constant pressure in container of 1 atm1 atm. The gas is compressed until temperature becomes 127℃. The work done isa)703 Jb)831.4 Jc)121 Jd)2035 JCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A container having 1 mole1 mole of a gas at a temperature 27℃ has a movable piston which maintains at constant pressure in container of 1 atm1 atm. The gas is compressed until temperature becomes 127℃. The work done isa)703 Jb)831.4 Jc)121 Jd)2035 JCorrect answer is option 'B'. Can you explain this answer?.
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