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An ideal monatomic gas is confined in a cylinder by a spring loaded with the massless piston of cross-section 8 × 10−3 m2. Piston can slide on the walls of the cylinder without any friction. Initially the gas is at 300 K300 K and occupies a volume of 2.4 × 10−3 m3 and the spring is in its relaxed position. Now, gas is slowly heated by a small electric heater and the piston moves out slowly by 0.1 m. Calculate the final temperature of the gas and the heat supplied by the heater. The force constant of the spring is 8000 N m−1 and atmospheric pressure 1 × 105 N m−2.
  • a)
    TF = 600 K, Q = 680 J
  • b)
    TF = 800 K, Q = 600 J
  • c)
    TF = 600 K, Q = 720 J
  • d)
    TF = 800 K, Q = 720 J
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
An ideal monatomic gas is confined in a cylinder by a spring loaded w...
As here initially,
PI = P0 = 1 × 105 N/m2, VI = V0 = 2.4 × 10-3 m3,
T1 = T0 = 300 K
​And finally,
= 2 × 105 N/m2
VF = V0 + Ax = 2.4 × 10-3 + 0.1 × 8 × 10-3
= 3.2 × 10-3 m3
So from gas equation PV = nRT, i.e.,
TF = 800 K
i.e., ΔW = 80 + 40 = 120 J
Note : 80 J of work is done against atmosphere and 40 J against spring.
Hence total heat supplied,
ΔQ = ΔU + ΔW = 600 + 120 = 720 J
Note : In this problem none of the variables F, P, V, T, U or Q is constant.
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The atmospheric lapse rateFor small volumes of gas, according to kinetic theory of gases, all parts of the gas are at the same temperature. But for huge volumes of gas like atmosphere, assumption of a uniform temperature throughout the gas is not valid. Different parts of the atmosphere are at different temperatures. Apart from the surface of the earth, variations also occur in temperature at different heights in the atmosphere.The decrease in temperature with height called the atmospheric lapse rate is similar at various locations across the surface of the Earth. By analyzing the data collected at various locations, it is found that average global lapse rate is – 6.7 °C/Km.The linear decrease with temperature only occurs in the lower part of the atmosphere called the troposphere. This is the part of the atmosphere in which weather occurs and our planes fly. Above the troposphere is the stratosphere, with an imaginary boundary separating the two layers. In the stratosphere, temperature tends to be relatively constant.Absorption of sunlight at the Earth’s surface warms the troposphere from below, so vertical convection currents are continually mixing in the air. As a parcel of air rises, its pressure drops and it expands. The parcel does work on its surrounding, so that its internal energy and therefore, its temperature drops. Assume that the vertical mixing is so rapid as to be adiabatic and the quantityTP(1 – λ)/λ has a uniform value through the layers of troposphere.(M is molecular mass of the air, R is universal gas constant, g is gravitational acc., P and T are pressure and temperature respectively at the point under consideration and y is height.)Q. Mechanical equilibrium of the atmosphere requires that the pressure decreases with altitude according to . Assuming free fall acceleration to be uniform, then lapse rate is given by

The atmospheric lapse rateFor small volumes of gas, according to kinetic theory of gases, all parts of the gas are at the same temperature. But for huge volumes of gas like atmosphere, assumption of a uniform temperature throughout the gas is not valid. Different parts of the atmosphere are at different temperatures. Apart from the surface of the earth, variations also occur in temperature at different heights in the atmosphere.The decrease in temperature with height called the atmospheric lapse rate is similar at various locations across the surface of the Earth. By analyzing the data collected at various locations, it is found that average global lapse rate is – 6.7 °C/Km.The linear decrease with temperature only occurs in the lower part of the atmosphere called the troposphere. This is the part of the atmosphere in which weather occurs and our planes fly. Above the troposphere is the stratosphere, with an imaginary boundary separating the two layers. In the stratosphere, temperature tends to be relatively constant.Absorption of sunlight at the Earth’s surface warms the troposphere from below, so vertical convection currents are continually mixing in the air. As a parcel of air rises, its pressure drops and it expands. The parcel does work on its surrounding, so that its internal energy and therefore, its temperature drops. Assume that the vertical mixing is so rapid as to be adiabatic and the quantityTP(1 – λ)/λ has a uniform value through the layers of troposphere.(M is molecular mass of the air, R is universal gas constant, g is gravitational acc., P and T are pressure and temperature respectively at the point under consideration and y is height.)Q. If behaviour of the mixing of parcels of air is approximately assumed to be adiabatic then lapse rate can be expressed as

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An ideal monatomic gas is confined in a cylinder by a spring loaded with the massless piston of cross-section 8 × 10−3 m2. Piston can slide on the walls of the cylinder without any friction. Initially the gas is at 300 K300 K and occupies a volume of 2.4 × 10−3 m3 and the spring is in its relaxed position. Now, gas is slowly heated by a small electric heater and the piston moves out slowly by 0.1 m. Calculate the final temperature of the gas and the heat supplied by the heater. The force constant of the spring is 8000 N m−1 and atmospheric pressure 1 × 105 N m−2.a)TF = 600 K, Q = 680 Jb)TF = 800 K, Q = 600 Jc)TF = 600 K, Q = 720 Jd)TF = 800 K, Q = 720 JCorrect answer is option 'D'. Can you explain this answer?
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An ideal monatomic gas is confined in a cylinder by a spring loaded with the massless piston of cross-section 8 × 10−3 m2. Piston can slide on the walls of the cylinder without any friction. Initially the gas is at 300 K300 K and occupies a volume of 2.4 × 10−3 m3 and the spring is in its relaxed position. Now, gas is slowly heated by a small electric heater and the piston moves out slowly by 0.1 m. Calculate the final temperature of the gas and the heat supplied by the heater. The force constant of the spring is 8000 N m−1 and atmospheric pressure 1 × 105 N m−2.a)TF = 600 K, Q = 680 Jb)TF = 800 K, Q = 600 Jc)TF = 600 K, Q = 720 Jd)TF = 800 K, Q = 720 JCorrect answer is option 'D'. 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 An ideal monatomic gas is confined in a cylinder by a spring loaded with the massless piston of cross-section 8 × 10−3 m2. Piston can slide on the walls of the cylinder without any friction. Initially the gas is at 300 K300 K and occupies a volume of 2.4 × 10−3 m3 and the spring is in its relaxed position. Now, gas is slowly heated by a small electric heater and the piston moves out slowly by 0.1 m. Calculate the final temperature of the gas and the heat supplied by the heater. The force constant of the spring is 8000 N m−1 and atmospheric pressure 1 × 105 N m−2.a)TF = 600 K, Q = 680 Jb)TF = 800 K, Q = 600 Jc)TF = 600 K, Q = 720 Jd)TF = 800 K, Q = 720 JCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ideal monatomic gas is confined in a cylinder by a spring loaded with the massless piston of cross-section 8 × 10−3 m2. Piston can slide on the walls of the cylinder without any friction. Initially the gas is at 300 K300 K and occupies a volume of 2.4 × 10−3 m3 and the spring is in its relaxed position. Now, gas is slowly heated by a small electric heater and the piston moves out slowly by 0.1 m. Calculate the final temperature of the gas and the heat supplied by the heater. The force constant of the spring is 8000 N m−1 and atmospheric pressure 1 × 105 N m−2.a)TF = 600 K, Q = 680 Jb)TF = 800 K, Q = 600 Jc)TF = 600 K, Q = 720 Jd)TF = 800 K, Q = 720 JCorrect answer is option 'D'. Can you explain this answer?.
Solutions for An ideal monatomic gas is confined in a cylinder by a spring loaded with the massless piston of cross-section 8 × 10−3 m2. Piston can slide on the walls of the cylinder without any friction. Initially the gas is at 300 K300 K and occupies a volume of 2.4 × 10−3 m3 and the spring is in its relaxed position. Now, gas is slowly heated by a small electric heater and the piston moves out slowly by 0.1 m. Calculate the final temperature of the gas and the heat supplied by the heater. The force constant of the spring is 8000 N m−1 and atmospheric pressure 1 × 105 N m−2.a)TF = 600 K, Q = 680 Jb)TF = 800 K, Q = 600 Jc)TF = 600 K, Q = 720 Jd)TF = 800 K, Q = 720 JCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
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