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Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35°C. The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol.K)
- a)62 J
- b)104 J
- c)124 J
- d)208 J
Correct answer is option 'D'. Can you explain this answer?
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Understanding the Problem
To calculate the heat required to raise the temperature of 2 moles of ideal helium gas from 30°C to 35°C, we can use the formula:
Q = n * C * ΔT
where:
- Q = heat added (in Joules)
- n = number of moles of gas
- C = molar heat capacity at constant volume for helium
- ΔT = change in temperature
Parameters
- Number of moles (n) = 2 moles
- Initial temperature (T1) = 30°C = 303 K
- Final temperature (T2) = 35°C = 308 K
- Change in temperature (ΔT) = T2 - T1 = 308 K - 303 K = 5 K
Calculating the Molar Heat Capacity
For an ideal monatomic gas like helium, the molar heat capacity at constant volume (C_V) is given by:
C_V = (3/2) * R
where R = 8.31 J/mol·K.
Now substituting the value of R:
C_V = (3/2) * 8.31 J/mol·K = 12.465 J/mol·K
Calculating the Heat Required
Now we can calculate the heat (Q):
Q = n * C_V * ΔT
Substituting the values:
- n = 2 moles
- C_V = 12.465 J/mol·K
- ΔT = 5 K
Q = 2 * 12.465 J/mol·K * 5 K
Q = 124.65 J
Since we round this value, we can say that the heat required is approximately 124 J.
Conclusion
Therefore, the correct option is:
c) 124 J
This implies that the answer provided in the question seems to have a misprint regarding the correct answer being option 'D', as our calculation leads us to option 'C'.
To calculate the heat required to raise the temperature of 2 moles of ideal helium gas from 30°C to 35°C, we can use the formula:
Q = n * C * ΔT
where:
- Q = heat added (in Joules)
- n = number of moles of gas
- C = molar heat capacity at constant volume for helium
- ΔT = change in temperature
Parameters
- Number of moles (n) = 2 moles
- Initial temperature (T1) = 30°C = 303 K
- Final temperature (T2) = 35°C = 308 K
- Change in temperature (ΔT) = T2 - T1 = 308 K - 303 K = 5 K
Calculating the Molar Heat Capacity
For an ideal monatomic gas like helium, the molar heat capacity at constant volume (C_V) is given by:
C_V = (3/2) * R
where R = 8.31 J/mol·K.
Now substituting the value of R:
C_V = (3/2) * 8.31 J/mol·K = 12.465 J/mol·K
Calculating the Heat Required
Now we can calculate the heat (Q):
Q = n * C_V * ΔT
Substituting the values:
- n = 2 moles
- C_V = 12.465 J/mol·K
- ΔT = 5 K
Q = 2 * 12.465 J/mol·K * 5 K
Q = 124.65 J
Since we round this value, we can say that the heat required is approximately 124 J.
Conclusion
Therefore, the correct option is:
c) 124 J
This implies that the answer provided in the question seems to have a misprint regarding the correct answer being option 'D', as our calculation leads us to option 'C'.
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Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandableand can be assumed to require no energy in its expansion. The temperature of the gas in theballoon is slowly changed to 35°C. The amount of heat required in raising the temperature isnearly (take R = 8.31 J/mol.K)a)62 Jb)104 Jc)124 Jd)208 JCorrect answer is option 'D'. Can you explain this answer?
Question Description
Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandableand can be assumed to require no energy in its expansion. The temperature of the gas in theballoon is slowly changed to 35°C. The amount of heat required in raising the temperature isnearly (take R = 8.31 J/mol.K)a)62 Jb)104 Jc)124 Jd)208 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 Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandableand can be assumed to require no energy in its expansion. The temperature of the gas in theballoon is slowly changed to 35°C. The amount of heat required in raising the temperature isnearly (take R = 8.31 J/mol.K)a)62 Jb)104 Jc)124 Jd)208 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 Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandableand can be assumed to require no energy in its expansion. The temperature of the gas in theballoon is slowly changed to 35°C. The amount of heat required in raising the temperature isnearly (take R = 8.31 J/mol.K)a)62 Jb)104 Jc)124 Jd)208 JCorrect answer is option 'D'. Can you explain this answer?.
Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandableand can be assumed to require no energy in its expansion. The temperature of the gas in theballoon is slowly changed to 35°C. The amount of heat required in raising the temperature isnearly (take R = 8.31 J/mol.K)a)62 Jb)104 Jc)124 Jd)208 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 Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandableand can be assumed to require no energy in its expansion. The temperature of the gas in theballoon is slowly changed to 35°C. The amount of heat required in raising the temperature isnearly (take R = 8.31 J/mol.K)a)62 Jb)104 Jc)124 Jd)208 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 Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandableand can be assumed to require no energy in its expansion. The temperature of the gas in theballoon is slowly changed to 35°C. The amount of heat required in raising the temperature isnearly (take R = 8.31 J/mol.K)a)62 Jb)104 Jc)124 Jd)208 JCorrect answer is option 'D'. Can you explain this answer?.
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