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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.?
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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.
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2) The speed of sound v in a gas might plausibly depend on the pressur...
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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.?
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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.?.
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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
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