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One mole of an ideal monoatomic gas requires 207 J heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is [Given the gas constant R = 8.3 J/ mol. K] [1990]
- a)198.7 J
- b)29 J
- c)215.3 J
- d)124 J
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
One mole of an ideal monoatomic gas requires 207 J heat to raise the t...
We know that Qv = nCvΔT and Qp = nCpΔT
Given Qp = 207 J 
Most Upvoted Answer
One mole of an ideal monoatomic gas requires 207 J heat to raise the t...
Given:
- Heat required to raise the temperature of 1 mole of an ideal monoatomic gas by 10 K at constant pressure = 207 J
- Gas constant, R = 8.3 J/mol.K
To find:
- Heat required to raise the temperature of the same gas by 10 K at constant volume
Solution:
1. Heat capacity at constant pressure (Cp) can be calculated as:
Cp = (ΔH / ΔT)p
where, ΔH = change in enthalpy, ΔT = change in temperature, and p = constant pressure
2. Heat capacity at constant volume (Cv) can be calculated as:
Cv = (ΔU / ΔT)v
where, ΔU = change in internal energy, and v = constant volume
For an ideal gas, internal energy depends only on temperature, so
ΔU = nCvΔT
where, n = number of moles of gas
3. The relationship between Cp and Cv for an ideal gas is:
Cp - Cv = nR
where, R = gas constant
Using these equations, we can find the heat required to raise the temperature of the gas at constant volume:
ΔU = nCvΔT
ΔH = ΔU + pΔV
where, ΔV = change in volume
At constant volume, ΔV = 0, so ΔH = ΔU
Cv = (ΔU / ΔT)v
ΔU = nCvΔT
Substituting these values,
Cv = (ΔU / ΔT)v = (ΔH / ΔT)v - pΔV / ΔT
Cp - Cv = nR
Cp = Cv + nR
ΔH = ΔU = nCvΔT
ΔH = nCpΔT - nRΔT
207 J = nCp(10 K) - nR(10 K)
nCp - nR = 20.7 J/mol
Cv = Cp - nR
Cv = 20.7 J/mol / n
For 1 mole of gas,
Cv = 20.7 J/mol
ΔU = nCvΔT = (1 mol)(20.7 J/mol)(10 K) = 207 J
Therefore, the heat required to raise the temperature of the gas by 10 K at constant volume is 207 J.
Answer: Option D (124 J) is incorrect.
- Heat required to raise the temperature of 1 mole of an ideal monoatomic gas by 10 K at constant pressure = 207 J
- Gas constant, R = 8.3 J/mol.K
To find:
- Heat required to raise the temperature of the same gas by 10 K at constant volume
Solution:
1. Heat capacity at constant pressure (Cp) can be calculated as:
Cp = (ΔH / ΔT)p
where, ΔH = change in enthalpy, ΔT = change in temperature, and p = constant pressure
2. Heat capacity at constant volume (Cv) can be calculated as:
Cv = (ΔU / ΔT)v
where, ΔU = change in internal energy, and v = constant volume
For an ideal gas, internal energy depends only on temperature, so
ΔU = nCvΔT
where, n = number of moles of gas
3. The relationship between Cp and Cv for an ideal gas is:
Cp - Cv = nR
where, R = gas constant
Using these equations, we can find the heat required to raise the temperature of the gas at constant volume:
ΔU = nCvΔT
ΔH = ΔU + pΔV
where, ΔV = change in volume
At constant volume, ΔV = 0, so ΔH = ΔU
Cv = (ΔU / ΔT)v
ΔU = nCvΔT
Substituting these values,
Cv = (ΔU / ΔT)v = (ΔH / ΔT)v - pΔV / ΔT
Cp - Cv = nR
Cp = Cv + nR
ΔH = ΔU = nCvΔT
ΔH = nCpΔT - nRΔT
207 J = nCp(10 K) - nR(10 K)
nCp - nR = 20.7 J/mol
Cv = Cp - nR
Cv = 20.7 J/mol / n
For 1 mole of gas,
Cv = 20.7 J/mol
ΔU = nCvΔT = (1 mol)(20.7 J/mol)(10 K) = 207 J
Therefore, the heat required to raise the temperature of the gas by 10 K at constant volume is 207 J.
Answer: Option D (124 J) is incorrect.
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One mole of an ideal monoatomic gas requires 207 J heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is [Given the gas constant R = 8.3 J/ mol. K] [1990]a)198.7 Jb)29 Jc)215.3 Jd)124 JCorrect answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about One mole of an ideal monoatomic gas requires 207 J heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is [Given the gas constant R = 8.3 J/ mol. K] [1990]a)198.7 Jb)29 Jc)215.3 Jd)124 JCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One mole of an ideal monoatomic gas requires 207 J heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is [Given the gas constant R = 8.3 J/ mol. K] [1990]a)198.7 Jb)29 Jc)215.3 Jd)124 JCorrect answer is option 'D'. Can you explain this answer?.
One mole of an ideal monoatomic gas requires 207 J heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is [Given the gas constant R = 8.3 J/ mol. K] [1990]a)198.7 Jb)29 Jc)215.3 Jd)124 JCorrect answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about One mole of an ideal monoatomic gas requires 207 J heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is [Given the gas constant R = 8.3 J/ mol. K] [1990]a)198.7 Jb)29 Jc)215.3 Jd)124 JCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One mole of an ideal monoatomic gas requires 207 J heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is [Given the gas constant R = 8.3 J/ mol. K] [1990]a)198.7 Jb)29 Jc)215.3 Jd)124 JCorrect answer is option 'D'. Can you explain this answer?.
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