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Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by 2.00 K.
- a)85.0 J
- b)95.0 J
- c)65.0 J
- d)75.0 J
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Calculate the change in internal energy of 3.00 mol of helium gas when...
Explanation:
Helium is a monoatomic gas.(CV = 1.5R)
change in internal energy
ΔU=nCVΔT=3×1.5×8.31×2=75J
Most Upvoted Answer
Calculate the change in internal energy of 3.00 mol of helium gas when...
Understanding Internal Energy Change
The internal energy change (ΔU) of an ideal gas can be calculated using the formula:
ΔU = n * C_v * ΔT
Where:
- n = number of moles
- C_v = molar specific heat at constant volume
- ΔT = change in temperature
Parameters for Helium Gas
- Helium is a monoatomic ideal gas.
- For monoatomic gases, C_v is approximately 3/2 R, where R is the ideal gas constant (8.314 J/mol·K).
Calculation Steps
1. Identify Variables:
- n = 3.00 mol (given)
- C_v = (3/2) * R = (3/2) * 8.314 J/mol·K = 12.471 J/mol·K
- ΔT = 2.00 K (given)
2. Plug in Values:
ΔU = n * C_v * ΔT
ΔU = 3.00 mol * 12.471 J/mol·K * 2.00 K
3. Perform the Calculation:
- ΔU = 3.00 * 12.471 * 2.00
- ΔU = 3.00 * 24.942
- ΔU = 74.826 J (approximately 75.0 J)
Conclusion
The calculated change in internal energy for 3.00 mol of helium gas when the temperature is increased by 2.00 K is approximately 75.0 J. Therefore, the correct answer is option 'D', which aligns with the calculated value.
The internal energy change (ΔU) of an ideal gas can be calculated using the formula:
ΔU = n * C_v * ΔT
Where:
- n = number of moles
- C_v = molar specific heat at constant volume
- ΔT = change in temperature
Parameters for Helium Gas
- Helium is a monoatomic ideal gas.
- For monoatomic gases, C_v is approximately 3/2 R, where R is the ideal gas constant (8.314 J/mol·K).
Calculation Steps
1. Identify Variables:
- n = 3.00 mol (given)
- C_v = (3/2) * R = (3/2) * 8.314 J/mol·K = 12.471 J/mol·K
- ΔT = 2.00 K (given)
2. Plug in Values:
ΔU = n * C_v * ΔT
ΔU = 3.00 mol * 12.471 J/mol·K * 2.00 K
3. Perform the Calculation:
- ΔU = 3.00 * 12.471 * 2.00
- ΔU = 3.00 * 24.942
- ΔU = 74.826 J (approximately 75.0 J)
Conclusion
The calculated change in internal energy for 3.00 mol of helium gas when the temperature is increased by 2.00 K is approximately 75.0 J. Therefore, the correct answer is option 'D', which aligns with the calculated value.
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Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by 2.00 K.a)85.0 Jb)95.0 Jc)65.0 Jd)75.0 JCorrect answer is option 'D'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by 2.00 K.a)85.0 Jb)95.0 Jc)65.0 Jd)75.0 JCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by 2.00 K.a)85.0 Jb)95.0 Jc)65.0 Jd)75.0 JCorrect answer is option 'D'. Can you explain this answer?.
Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by 2.00 K.a)85.0 Jb)95.0 Jc)65.0 Jd)75.0 JCorrect answer is option 'D'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by 2.00 K.a)85.0 Jb)95.0 Jc)65.0 Jd)75.0 JCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by 2.00 K.a)85.0 Jb)95.0 Jc)65.0 Jd)75.0 JCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by 2.00 K.a)85.0 Jb)95.0 Jc)65.0 Jd)75.0 JCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
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