Class 11 Exam > Class 11 Questions > 2) The speed of sound v in a gas might plausi...
Start Learning for Free
2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.?
Most Upvoted Answer
2) The speed of sound v in a gas might plausibly depend on the pressur...
Dimensional Analysis:
Dimensional analysis is a powerful tool used in physics to derive the relationship between different physical quantities. In this case, we need to determine the exponents x, y, and z in the formula v = C p x ρ y V z using dimensional analysis.
Step 1: List the dimensions of each variable
The dimensions of pressure are [M][L]-1[T]-2, where M is mass, L is length, and T is time. The dimensions of density are [M][L]-3, and the dimensions of volume are [L]3. The dimensions of velocity are [L][T]-1.
Step 2: Equate the dimensions on both sides of the equation
Equating the dimensions on both sides of the equation, we get:
[L][T]-1 = [M]x [L]-3y [L]3z
Simplifying, we get:
x = 0
y = 1/2
z = 1/2
Step 3: Determine the value of the constant C
To determine the value of the constant C, we need to use experimental data. However, we can make an educated guess based on the physical properties of the gas. The speed of sound in a gas is determined by the elastic properties of the gas molecules and their interactions with each other. Therefore, we can assume that the value of C is proportional to the square root of the average kinetic energy of the gas molecules, which is proportional to the temperature of the gas.
Conclusion:
Using dimensional analysis, we have determined the exponents x, y, and z in the formula v = C p x ρ y V z to be x = 0, y = 1/2, and z = 1/2. The value of the constant C depends on the physical properties of the gas and can be determined experimentally.
Dimensional analysis is a powerful tool used in physics to derive the relationship between different physical quantities. In this case, we need to determine the exponents x, y, and z in the formula v = C p x ρ y V z using dimensional analysis.
Step 1: List the dimensions of each variable
The dimensions of pressure are [M][L]-1[T]-2, where M is mass, L is length, and T is time. The dimensions of density are [M][L]-3, and the dimensions of volume are [L]3. The dimensions of velocity are [L][T]-1.
Step 2: Equate the dimensions on both sides of the equation
Equating the dimensions on both sides of the equation, we get:
[L][T]-1 = [M]x [L]-3y [L]3z
Simplifying, we get:
x = 0
y = 1/2
z = 1/2
Step 3: Determine the value of the constant C
To determine the value of the constant C, we need to use experimental data. However, we can make an educated guess based on the physical properties of the gas. The speed of sound in a gas is determined by the elastic properties of the gas molecules and their interactions with each other. Therefore, we can assume that the value of C is proportional to the square root of the average kinetic energy of the gas molecules, which is proportional to the temperature of the gas.
Conclusion:
Using dimensional analysis, we have determined the exponents x, y, and z in the formula v = C p x ρ y V z to be x = 0, y = 1/2, and z = 1/2. The value of the constant C depends on the physical properties of the gas and can be determined experimentally.
Community Answer
2) The speed of sound v in a gas might plausibly depend on the pressur...
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.?
Question Description
2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.?.
2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.?.
Solutions for 2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of 2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.? defined & explained in the simplest way possible. Besides giving the explanation of
2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.?, a detailed solution for 2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.? has been provided alongside types of 2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.? theory, EduRev gives you an
ample number of questions to practice 2) The speed of sound v in a gas might plausibly depend on the pressure p, the density ρ, and the volume V of the gas. Use dimensional analysis to determine the exponents x, y, and z in the formula v = C p x ρ y V z , where C is a dimensionless constant. Incidentally, the mks units of pressure are kilograms per meter per second square.? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
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