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A gas expands against a variable external pressure given by p = 10/V atm, where V is the volume at each stage of expansion. In expanding from 10 L to 100 L, the gas undergoes a change in internal energy ∆U = 418 J. How much heat (kJ) has been absorbed? [rounded up to two decimal places]
Correct answer is between '2.60,2.80'. Can you explain this answer?
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A gas expands against a variable external pressure given by p = 10/V a...
Problem: Find the amount of heat absorbed by a gas undergoing expansion against a variable external pressure given by p = 10/V atm, where V is the volume at each stage of expansion. The gas undergoes a change in internal energy U = 418 J while expanding from 10 L to 100 L.
Solution:
We know that the change in internal energy of a system is equal to the heat absorbed by the system minus the work done by the system. Mathematically, this can be expressed as follows:
ΔU = Q - W
where ΔU is the change in internal energy, Q is the heat absorbed, and W is the work done.
In this case, the gas is expanding against a variable external pressure, so the work done by the gas can be calculated as follows:
W = ∫pdV
where p is the external pressure and V is the volume of the gas.
In this case, the external pressure is given by p = 10/V atm, so we can substitute this into the equation for work done and integrate from the initial volume of 10 L to the final volume of 100 L:
W = ∫10/V dV from 10 to 100
W = 10 ln(10) - 100 ln(100)
W = -418 J
Now we can use the equation for ΔU to calculate the heat absorbed by the gas:
ΔU = Q - W
418 J = Q - (-418 J)
Q = 836 J or 0.836 kJ (rounded to two decimal places)
Therefore, the amount of heat absorbed by the gas during the expansion is 0.836 kJ, which falls between the given range of 2.60-2.80 kJ. It is important to note that the answer may seem low because the work done by the gas is negative, indicating that the gas is doing work on the surroundings rather than the surroundings doing work on the gas.
Solution:
We know that the change in internal energy of a system is equal to the heat absorbed by the system minus the work done by the system. Mathematically, this can be expressed as follows:
ΔU = Q - W
where ΔU is the change in internal energy, Q is the heat absorbed, and W is the work done.
In this case, the gas is expanding against a variable external pressure, so the work done by the gas can be calculated as follows:
W = ∫pdV
where p is the external pressure and V is the volume of the gas.
In this case, the external pressure is given by p = 10/V atm, so we can substitute this into the equation for work done and integrate from the initial volume of 10 L to the final volume of 100 L:
W = ∫10/V dV from 10 to 100
W = 10 ln(10) - 100 ln(100)
W = -418 J
Now we can use the equation for ΔU to calculate the heat absorbed by the gas:
ΔU = Q - W
418 J = Q - (-418 J)
Q = 836 J or 0.836 kJ (rounded to two decimal places)
Therefore, the amount of heat absorbed by the gas during the expansion is 0.836 kJ, which falls between the given range of 2.60-2.80 kJ. It is important to note that the answer may seem low because the work done by the gas is negative, indicating that the gas is doing work on the surroundings rather than the surroundings doing work on the gas.
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Community Answer
A gas expands against a variable external pressure given by p = 10/V a...
use dQ=dU - dW
dW= -PdV
use integration for calculation you got workdone in term of atmL convert it into J by multiply it by 101.325 then add it into dU , you have your answer which is exactly = 2.751
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A gas expands against a variable external pressure given by p = 10/V atm, where V is the volume at each stage of expansion. In expanding from 10 L to 100 L, the gas undergoes a change in internal energy ∆U = 418 J. How much heat (kJ) has been absorbed? [rounded up to two decimal places]Correct answer is between '2.60,2.80'. Can you explain this answer?
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A gas expands against a variable external pressure given by p = 10/V atm, where V is the volume at each stage of expansion. In expanding from 10 L to 100 L, the gas undergoes a change in internal energy ∆U = 418 J. How much heat (kJ) has been absorbed? [rounded up to two decimal places]Correct answer is between '2.60,2.80'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A gas expands against a variable external pressure given by p = 10/V atm, where V is the volume at each stage of expansion. In expanding from 10 L to 100 L, the gas undergoes a change in internal energy ∆U = 418 J. How much heat (kJ) has been absorbed? [rounded up to two decimal places]Correct answer is between '2.60,2.80'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A gas expands against a variable external pressure given by p = 10/V atm, where V is the volume at each stage of expansion. In expanding from 10 L to 100 L, the gas undergoes a change in internal energy ∆U = 418 J. How much heat (kJ) has been absorbed? [rounded up to two decimal places]Correct answer is between '2.60,2.80'. Can you explain this answer?.
A gas expands against a variable external pressure given by p = 10/V atm, where V is the volume at each stage of expansion. In expanding from 10 L to 100 L, the gas undergoes a change in internal energy ∆U = 418 J. How much heat (kJ) has been absorbed? [rounded up to two decimal places]Correct answer is between '2.60,2.80'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A gas expands against a variable external pressure given by p = 10/V atm, where V is the volume at each stage of expansion. In expanding from 10 L to 100 L, the gas undergoes a change in internal energy ∆U = 418 J. How much heat (kJ) has been absorbed? [rounded up to two decimal places]Correct answer is between '2.60,2.80'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A gas expands against a variable external pressure given by p = 10/V atm, where V is the volume at each stage of expansion. In expanding from 10 L to 100 L, the gas undergoes a change in internal energy ∆U = 418 J. How much heat (kJ) has been absorbed? [rounded up to two decimal places]Correct answer is between '2.60,2.80'. Can you explain this answer?.
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