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The corrected gas equation is a cubic in v, which of the following statement is true about its roots?
- a)at low temperature, three positive real roots exists
- b)at critical temperature, the three real roots become equal
- c)at high temperature, only one real root exists
- d)all of the mentioned
Correct answer is option 'D'. Can you explain this answer?
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The corrected gas equation is a cubic in v, which of the following sta...
The equation has three roots which are different for different temperature and pressure.
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The corrected gas equation is a cubic in v, which of the following sta...
Explanation:
The corrected gas equation in terms of volume (v) is given by:
P(v - b) = RT
where P is the pressure, T is the temperature, R is the gas constant, and b is a constant that accounts for the volume occupied by the gas particles.
Statement a) At low temperature, three positive real roots exist:
At low temperatures, the term RT in the equation is small compared to P(v - b), resulting in a cubic equation with three distinct real roots. This is because the pressure term dominates, and the volume term can vary to give different solutions.
Statement b) At critical temperature, the three real roots become equal:
The critical temperature is the temperature above which a gas cannot be liquefied, regardless of the pressure applied. At this temperature, the attractive and repulsive forces between gas particles become equal, resulting in the disappearance of any distinct real roots. The equation reduces to a single root, where the volume of the gas approaches infinity.
Statement c) At high temperature, only one real root exists:
At high temperatures, the term RT dominates over P(v - b) in the equation. As a result, the equation reduces to a linear equation with only one real root. This is because the volume term becomes negligible compared to the temperature term.
Conclusion:
From the above explanations, it can be concluded that all the given statements are true. At low temperatures, three positive real roots exist; at critical temperature, the three real roots become equal; and at high temperatures, only one real root exists. Therefore, the correct answer is option 'D' - all of the mentioned.
The corrected gas equation in terms of volume (v) is given by:
P(v - b) = RT
where P is the pressure, T is the temperature, R is the gas constant, and b is a constant that accounts for the volume occupied by the gas particles.
Statement a) At low temperature, three positive real roots exist:
At low temperatures, the term RT in the equation is small compared to P(v - b), resulting in a cubic equation with three distinct real roots. This is because the pressure term dominates, and the volume term can vary to give different solutions.
Statement b) At critical temperature, the three real roots become equal:
The critical temperature is the temperature above which a gas cannot be liquefied, regardless of the pressure applied. At this temperature, the attractive and repulsive forces between gas particles become equal, resulting in the disappearance of any distinct real roots. The equation reduces to a single root, where the volume of the gas approaches infinity.
Statement c) At high temperature, only one real root exists:
At high temperatures, the term RT dominates over P(v - b) in the equation. As a result, the equation reduces to a linear equation with only one real root. This is because the volume term becomes negligible compared to the temperature term.
Conclusion:
From the above explanations, it can be concluded that all the given statements are true. At low temperatures, three positive real roots exist; at critical temperature, the three real roots become equal; and at high temperatures, only one real root exists. Therefore, the correct answer is option 'D' - all of the mentioned.
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The corrected gas equation is a cubic in v, which of the following statement is true about its roots?a)at low temperature, three positive real roots existsb)at critical temperature, the three real roots become equalc)at high temperature, only one real root existsd)all of the mentionedCorrect answer is option 'D'. Can you explain this answer?
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The corrected gas equation is a cubic in v, which of the following statement is true about its roots?a)at low temperature, three positive real roots existsb)at critical temperature, the three real roots become equalc)at high temperature, only one real root existsd)all of the mentionedCorrect answer is option 'D'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The corrected gas equation is a cubic in v, which of the following statement is true about its roots?a)at low temperature, three positive real roots existsb)at critical temperature, the three real roots become equalc)at high temperature, only one real root existsd)all of the mentionedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The corrected gas equation is a cubic in v, which of the following statement is true about its roots?a)at low temperature, three positive real roots existsb)at critical temperature, the three real roots become equalc)at high temperature, only one real root existsd)all of the mentionedCorrect answer is option 'D'. Can you explain this answer?.
The corrected gas equation is a cubic in v, which of the following statement is true about its roots?a)at low temperature, three positive real roots existsb)at critical temperature, the three real roots become equalc)at high temperature, only one real root existsd)all of the mentionedCorrect answer is option 'D'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The corrected gas equation is a cubic in v, which of the following statement is true about its roots?a)at low temperature, three positive real roots existsb)at critical temperature, the three real roots become equalc)at high temperature, only one real root existsd)all of the mentionedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The corrected gas equation is a cubic in v, which of the following statement is true about its roots?a)at low temperature, three positive real roots existsb)at critical temperature, the three real roots become equalc)at high temperature, only one real root existsd)all of the mentionedCorrect answer is option 'D'. Can you explain this answer?.
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