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The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol.K). When the temperature increases by 100K, the change in molar specific enthalpy is _______________ J/mol.
Correct answer is between '2908,2911'. Can you explain this answer?
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The molar specific heat at constant volume of an ideal gas is equal to...
The molar specific heat at constant volume, denoted as Cv, is defined as the amount of heat required to raise the temperature of one mole of a substance by 1 Kelvin (or 1 degree Celsius) at constant volume. In the case of an ideal gas, Cv is related to the universal gas constant, R, by the equation:
Cv = R / (γ - 1)
where γ is the adiabatic index or heat capacity ratio, defined as the ratio of the specific heat at constant pressure (Cp) to the specific heat at constant volume (Cv).
Given that Cv = 2.5 * R, we can substitute this value into the equation to find γ:
2.5 * R = R / (γ - 1)
Multiplying both sides by (γ - 1), we get:
2.5 * R * (γ - 1) = R
Expanding the equation:
2.5 * R * γ - 2.5 * R = R
Rearranging the terms:
2.5 * R * γ = 3.5 * R
Dividing both sides by 2.5 * R, we find:
γ = 3.5 / 2.5
γ = 1.4
So, the adiabatic index for this gas is 1.4.
Now, to find the change in molar specific enthalpy (ΔH) when the temperature increases by 100K, we can use the equation:
ΔH = Cp * ΔT
where Cp is the molar specific heat at constant pressure and ΔT is the change in temperature.
In the case of an ideal gas, Cp is related to Cv and R by the equation:
Cp = γ * Cv
Substituting the given values, Cp = 1.4 * Cv, into the equation, we have:
ΔH = 1.4 * Cv * ΔT
ΔH = 1.4 * (2.5 * R) * ΔT
Since ΔT = 100K, we can substitute the value of R (8.314 J/mol.K) into the equation:
ΔH = 1.4 * (2.5 * 8.314 J/mol.K) * 100K
Calculating the expression:
ΔH ≈ 2909.95 J/mol
Therefore, the change in molar specific enthalpy is approximately 2909.95 J/mol, which falls within the given range of 2908-2911 J/mol.
Cv = R / (γ - 1)
where γ is the adiabatic index or heat capacity ratio, defined as the ratio of the specific heat at constant pressure (Cp) to the specific heat at constant volume (Cv).
Given that Cv = 2.5 * R, we can substitute this value into the equation to find γ:
2.5 * R = R / (γ - 1)
Multiplying both sides by (γ - 1), we get:
2.5 * R * (γ - 1) = R
Expanding the equation:
2.5 * R * γ - 2.5 * R = R
Rearranging the terms:
2.5 * R * γ = 3.5 * R
Dividing both sides by 2.5 * R, we find:
γ = 3.5 / 2.5
γ = 1.4
So, the adiabatic index for this gas is 1.4.
Now, to find the change in molar specific enthalpy (ΔH) when the temperature increases by 100K, we can use the equation:
ΔH = Cp * ΔT
where Cp is the molar specific heat at constant pressure and ΔT is the change in temperature.
In the case of an ideal gas, Cp is related to Cv and R by the equation:
Cp = γ * Cv
Substituting the given values, Cp = 1.4 * Cv, into the equation, we have:
ΔH = 1.4 * Cv * ΔT
ΔH = 1.4 * (2.5 * R) * ΔT
Since ΔT = 100K, we can substitute the value of R (8.314 J/mol.K) into the equation:
ΔH = 1.4 * (2.5 * 8.314 J/mol.K) * 100K
Calculating the expression:
ΔH ≈ 2909.95 J/mol
Therefore, the change in molar specific enthalpy is approximately 2909.95 J/mol, which falls within the given range of 2908-2911 J/mol.
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The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol.K). When the temperature increases by 100K, the change in molar specific enthalpy is _______________ J/mol.Correct answer is between '2908,2911'. Can you explain this answer?
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The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol.K). When the temperature increases by 100K, the change in molar specific enthalpy is _______________ J/mol.Correct answer is between '2908,2911'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol.K). When the temperature increases by 100K, the change in molar specific enthalpy is _______________ J/mol.Correct answer is between '2908,2911'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol.K). When the temperature increases by 100K, the change in molar specific enthalpy is _______________ J/mol.Correct answer is between '2908,2911'. Can you explain this answer?.
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