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When 0.5 mole of a gas expands isothermally and reversible from a volume of 2L to 5L at 300K the change in internal energy if 200 cal of heat is absorbed?
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When 0.5 mole of a gas expands isothermally and reversible from a volu...
Introduction:
The problem involves calculating the change in internal energy of a gas which expands isothermally and reversibly from a volume of 2L to 5L at 300K. The amount of heat absorbed during the process is given as 200 cal.
Formula:
The change in internal energy (ΔU) of a gas is given by the formula:
ΔU = q + w
where q is the heat absorbed by the system and w is the work done by the system. For an isothermal and reversible expansion, the work done by the system is given by:
w = -nRT ln(Vf/Vi)
where n is the number of moles of gas, R is the gas constant, T is the temperature in Kelvin, Vf is the final volume and Vi is the initial volume.
Calculation:
Given,
n = 0.5 mole
Vi = 2L
Vf = 5L
T = 300K
q = 200 cal
Using the formula for work done, we get:
w = -nRT ln(Vf/Vi)
w = -0.5 * 8.314 * 300 * ln(5/2)
w = -623.34 J
Converting the heat absorbed from calories to Joules, we get:
q = 200 * 4.184
q = 836.8 J
Substituting the values of q and w in the formula for change in internal energy, we get:
ΔU = q + w
ΔU = 836.8 - 623.34
ΔU = 213.46 J
Therefore, the change in internal energy of the gas is 213.46 J.
Conclusion:
The change in internal energy of a gas which expands isothermally and reversibly from a volume of 2L to 5L at 300K, absorbing 200 cal of heat is 213.46 J.
The problem involves calculating the change in internal energy of a gas which expands isothermally and reversibly from a volume of 2L to 5L at 300K. The amount of heat absorbed during the process is given as 200 cal.
Formula:
The change in internal energy (ΔU) of a gas is given by the formula:
ΔU = q + w
where q is the heat absorbed by the system and w is the work done by the system. For an isothermal and reversible expansion, the work done by the system is given by:
w = -nRT ln(Vf/Vi)
where n is the number of moles of gas, R is the gas constant, T is the temperature in Kelvin, Vf is the final volume and Vi is the initial volume.
Calculation:
Given,
n = 0.5 mole
Vi = 2L
Vf = 5L
T = 300K
q = 200 cal
Using the formula for work done, we get:
w = -nRT ln(Vf/Vi)
w = -0.5 * 8.314 * 300 * ln(5/2)
w = -623.34 J
Converting the heat absorbed from calories to Joules, we get:
q = 200 * 4.184
q = 836.8 J
Substituting the values of q and w in the formula for change in internal energy, we get:
ΔU = q + w
ΔU = 836.8 - 623.34
ΔU = 213.46 J
Therefore, the change in internal energy of the gas is 213.46 J.
Conclusion:
The change in internal energy of a gas which expands isothermally and reversibly from a volume of 2L to 5L at 300K, absorbing 200 cal of heat is 213.46 J.
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When 0.5 mole of a gas expands isothermally and reversible from a volume of 2L to 5L at 300K the change in internal energy if 200 cal of heat is absorbed?
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When 0.5 mole of a gas expands isothermally and reversible from a volume of 2L to 5L at 300K the change in internal energy if 200 cal of heat is absorbed? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about When 0.5 mole of a gas expands isothermally and reversible from a volume of 2L to 5L at 300K the change in internal energy if 200 cal of heat is absorbed? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When 0.5 mole of a gas expands isothermally and reversible from a volume of 2L to 5L at 300K the change in internal energy if 200 cal of heat is absorbed?.
When 0.5 mole of a gas expands isothermally and reversible from a volume of 2L to 5L at 300K the change in internal energy if 200 cal of heat is absorbed? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about When 0.5 mole of a gas expands isothermally and reversible from a volume of 2L to 5L at 300K the change in internal energy if 200 cal of heat is absorbed? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When 0.5 mole of a gas expands isothermally and reversible from a volume of 2L to 5L at 300K the change in internal energy if 200 cal of heat is absorbed?.
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