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Statement-1 : Molar heat capacity of an ideal monoatomic gas at constant volume is a constant at all temperatures.
Statement-2 : As the temperature of an monoatomic ideal gas is increased, number of degrees of freedom of gas molecules remains constant.
- a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
- b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
- c)Statement-1 is True, Statement-2 is False
- d)Statement-1 is False, Statement-2 is True
Correct answer is option 'A'. Can you explain this answer?
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Statement-1 : Molar heat capacity of an ideal monoatomic gas at consta...
For monoatomic gas the degrees of freedom are only translational and hence do not depend on temperature. Therefore molar heat capacity of an ideal monoatomic gas at constant volume is a constant at all temperatures.
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Statement-1 : Molar heat capacity of an ideal monoatomic gas at consta...
Understanding Molar Heat Capacity
The molar heat capacity of an ideal monoatomic gas at constant volume is a key concept in thermodynamics.
- Molar Heat Capacity at Constant Volume (Cv): For an ideal monoatomic gas, Cv is given by (3/2)R, where R is the universal gas constant. This value remains constant at all temperatures because the energy associated with the translational degrees of freedom does not change with temperature.
Degrees of Freedom
- Degrees of Freedom for Monoatomic Gases: Monoatomic gases have three translational degrees of freedom (movement in the x, y, and z directions), and they do not possess rotational or vibrational degrees of freedom.
- Temperature Independence: As temperature increases, the number of degrees of freedom for monoatomic gas molecules remains constant at three. This is because the structure of a monoatomic gas does not allow for additional degrees of freedom.
Explanation of the Statements
- Statement-1 (True): The molar heat capacity at constant volume is a constant value (3/2)R for monoatomic gases, regardless of temperature.
- Statement-2 (True): The number of degrees of freedom remains constant (three) as the temperature increases.
Correct Relationship
- Statement-2 as Explanation: The constancy of the molar heat capacity (Statement-1) is directly tied to the constancy of degrees of freedom (Statement-2). Since the energy associated with these degrees of freedom does not change with temperature, Statement-2 provides a correct explanation for Statement-1.
Thus, the correct answer is option 'A': both statements are true, and Statement-2 correctly explains Statement-1.
The molar heat capacity of an ideal monoatomic gas at constant volume is a key concept in thermodynamics.
- Molar Heat Capacity at Constant Volume (Cv): For an ideal monoatomic gas, Cv is given by (3/2)R, where R is the universal gas constant. This value remains constant at all temperatures because the energy associated with the translational degrees of freedom does not change with temperature.
Degrees of Freedom
- Degrees of Freedom for Monoatomic Gases: Monoatomic gases have three translational degrees of freedom (movement in the x, y, and z directions), and they do not possess rotational or vibrational degrees of freedom.
- Temperature Independence: As temperature increases, the number of degrees of freedom for monoatomic gas molecules remains constant at three. This is because the structure of a monoatomic gas does not allow for additional degrees of freedom.
Explanation of the Statements
- Statement-1 (True): The molar heat capacity at constant volume is a constant value (3/2)R for monoatomic gases, regardless of temperature.
- Statement-2 (True): The number of degrees of freedom remains constant (three) as the temperature increases.
Correct Relationship
- Statement-2 as Explanation: The constancy of the molar heat capacity (Statement-1) is directly tied to the constancy of degrees of freedom (Statement-2). Since the energy associated with these degrees of freedom does not change with temperature, Statement-2 provides a correct explanation for Statement-1.
Thus, the correct answer is option 'A': both statements are true, and Statement-2 correctly explains Statement-1.
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Statement-1 : Molar heat capacity of an ideal monoatomic gas at constant volume is a constant at all temperatures.Statement-2 : As the temperature of an monoatomic ideal gas is increased, number of degrees of freedom of gas molecules remains constant.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'A'. Can you explain this answer?
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Statement-1 : Molar heat capacity of an ideal monoatomic gas at constant volume is a constant at all temperatures.Statement-2 : As the temperature of an monoatomic ideal gas is increased, number of degrees of freedom of gas molecules remains constant.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'A'. 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 Statement-1 : Molar heat capacity of an ideal monoatomic gas at constant volume is a constant at all temperatures.Statement-2 : As the temperature of an monoatomic ideal gas is increased, number of degrees of freedom of gas molecules remains constant.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statement-1 : Molar heat capacity of an ideal monoatomic gas at constant volume is a constant at all temperatures.Statement-2 : As the temperature of an monoatomic ideal gas is increased, number of degrees of freedom of gas molecules remains constant.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'A'. Can you explain this answer?.
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