Physics Exam > Physics Questions > During an experiment, an ideal gas is found t...
Start Learning for Free
During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .
Correct answer is '1.4'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
During an experiment, an ideal gas is found to obey an additional law ...
vp2 = constant
putting ,
we have T2/V = constant
or T∝√V
so , if V is doubled , T becomes √2 = 1.4times.
putting ,
we have T2/V = constantor T∝√V
so , if V is doubled , T becomes √2 = 1.4times.
Most Upvoted Answer
During an experiment, an ideal gas is found to obey an additional law ...
vp2 = constant
putting , we have T2/V = constant
or T∝√V
so , if V is doubled , T becomes √2 = 1.4times.
putting ,
we have T2/V = constantor T∝√V
so , if V is doubled , T becomes √2 = 1.4times.
Free Test
FREE
| Start Free Test |
Community Answer
During an experiment, an ideal gas is found to obey an additional law ...
Understanding the Given Law
In this experiment, the ideal gas follows the law \( p^2 V = \text{constant} \). This implies a relationship between pressure (p), volume (V), and temperature (T) of the gas.
Initial Conditions
- The initial conditions are:
- Pressure: \( p_1 \)
- Volume: \( V \)
- Temperature: \( T \)
From the ideal gas law, we know:
\[ p_1 V = nRT \]
Where \( n \) is the number of moles and \( R \) is the gas constant.
Final Conditions After Expansion
After expanding to volume \( 2V \), let the final pressure be \( p_2 \) and the final temperature be \( T_f \):
- New volume: \( 2V \)
- Applying the given law at the final state:
\[ p_2^2 (2V) = p_1^2 V \]
From this, we can derive:
\[ p_2^2 = \frac{p_1^2 V}{2V} = \frac{p_1^2}{2} \]
Thus:
\[ p_2 = \frac{p_1}{\sqrt{2}} \]
Applying the Ideal Gas Law
Now, applying the ideal gas law to the final state:
\[ p_2 (2V) = nRT_f \]
Substituting for \( p_2 \):
\[ \frac{p_1}{\sqrt{2}} (2V) = nRT_f \]
Equating with the initial state:
\[ p_1 V = nRT \]
We can solve for \( T_f \):
\[ \frac{2p_1 V}{\sqrt{2}} = nRT_f \]
Substituting \( p_1 V \):
\[ \frac{2(nRT)}{\sqrt{2}} = nRT_f \]
Simplifying gives:
\[ T_f = \frac{2T}{\sqrt{2}} = T \sqrt{2} \]
To find the numerical temperature, if \( T \) is normalized to 1, then:
\[ T_f = 1 \cdot \sqrt{2} \approx 1.4 \]
Conclusion
Hence, when the gas expands to volume \( 2V \), the final temperature becomes approximately 1.4.
In this experiment, the ideal gas follows the law \( p^2 V = \text{constant} \). This implies a relationship between pressure (p), volume (V), and temperature (T) of the gas.
Initial Conditions
- The initial conditions are:
- Pressure: \( p_1 \)
- Volume: \( V \)
- Temperature: \( T \)
From the ideal gas law, we know:
\[ p_1 V = nRT \]
Where \( n \) is the number of moles and \( R \) is the gas constant.
Final Conditions After Expansion
After expanding to volume \( 2V \), let the final pressure be \( p_2 \) and the final temperature be \( T_f \):
- New volume: \( 2V \)
- Applying the given law at the final state:
\[ p_2^2 (2V) = p_1^2 V \]
From this, we can derive:
\[ p_2^2 = \frac{p_1^2 V}{2V} = \frac{p_1^2}{2} \]
Thus:
\[ p_2 = \frac{p_1}{\sqrt{2}} \]
Applying the Ideal Gas Law
Now, applying the ideal gas law to the final state:
\[ p_2 (2V) = nRT_f \]
Substituting for \( p_2 \):
\[ \frac{p_1}{\sqrt{2}} (2V) = nRT_f \]
Equating with the initial state:
\[ p_1 V = nRT \]
We can solve for \( T_f \):
\[ \frac{2p_1 V}{\sqrt{2}} = nRT_f \]
Substituting \( p_1 V \):
\[ \frac{2(nRT)}{\sqrt{2}} = nRT_f \]
Simplifying gives:
\[ T_f = \frac{2T}{\sqrt{2}} = T \sqrt{2} \]
To find the numerical temperature, if \( T \) is normalized to 1, then:
\[ T_f = 1 \cdot \sqrt{2} \approx 1.4 \]
Conclusion
Hence, when the gas expands to volume \( 2V \), the final temperature becomes approximately 1.4.
|
Explore Courses for Physics exam
|
|
Similar Physics Doubts
During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer?
Question Description
During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer?.
During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer?.
Solutions for During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer?, a detailed solution for During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer? has been provided alongside types of During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice During an experiment, an ideal gas is found to obey an additional law p2V = constant. The gas is initially at a temperature T and volume V. When it expands to a volume 2V. the temperature becomes ____ .Correct answer is '1.4'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup