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A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R - a). For a≪R the magnitude of the work done in the process is given by (4πp0R2)X, where X is a constant and γ = Cp/Cv = 41/30. The value of X is________.
Correct answer is '2.05'. Can you explain this answer?
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A spherical bubble inside water has radius R. Take the pressure inside...
= W = (ΔP)avg x 4πR2a
{for small change (ΔP)avg <P> arithmetic mean}
{for small change (ΔP)avg <P> arithmetic mean}
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A spherical bubble inside water has radius R. Take the pressure inside...
/3)πR^3(p0 + (4/3)p0a/R) - (4/3)π(R-a)^3(p0 + (4/3)p0a/(R-a)).
To find the work done, we need to calculate the change in energy of the system. Since the process is adiabatic, there is no heat transfer and the change in energy is solely due to work.
Initially, the energy of the system is given by:
E1 = (4/3)πR^3p0
After compression, the energy becomes:
E2 = (4/3)π(R-a)^3p0
The work done is therefore:
W = E1 - E2
= (4/3)πR^3p0 - (4/3)π(R-a)^3p0
= (4/3)πp0(R^3 - (R-a)^3)
Expanding the cube of (R-a), we get:
W = (4/3)πp0(R^3 - R^3 + 3R^2a - 3Ra^2 + a^3)
= (4/3)πp0(3R^2a - 3Ra^2 + a^3)
Factoring out a^2 and simplifying, we get:
W = (4/3)πp0a^2(R - a) (3R + 3a)
Finally, substituting aR in the expression, we get:
W = (4/3)πp0a^2(R - a) (3R + 3a)
= (4/3)πp0a^2R(R - a)(3 + 3a/R)
Therefore, the magnitude of the work done in the process is given by:
|(4/3)πp0a^2R(R - a)(3 + 3a/R)| = (4/3)πp0a^2R(R - a)(3 + 3a/R)
To find the work done, we need to calculate the change in energy of the system. Since the process is adiabatic, there is no heat transfer and the change in energy is solely due to work.
Initially, the energy of the system is given by:
E1 = (4/3)πR^3p0
After compression, the energy becomes:
E2 = (4/3)π(R-a)^3p0
The work done is therefore:
W = E1 - E2
= (4/3)πR^3p0 - (4/3)π(R-a)^3p0
= (4/3)πp0(R^3 - (R-a)^3)
Expanding the cube of (R-a), we get:
W = (4/3)πp0(R^3 - R^3 + 3R^2a - 3Ra^2 + a^3)
= (4/3)πp0(3R^2a - 3Ra^2 + a^3)
Factoring out a^2 and simplifying, we get:
W = (4/3)πp0a^2(R - a) (3R + 3a)
Finally, substituting aR in the expression, we get:
W = (4/3)πp0a^2(R - a) (3R + 3a)
= (4/3)πp0a^2R(R - a)(3 + 3a/R)
Therefore, the magnitude of the work done in the process is given by:
|(4/3)πp0a^2R(R - a)(3 + 3a/R)| = (4/3)πp0a^2R(R - a)(3 + 3a/R)
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A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R - a). For aRthe magnitude of the work done in the process is given by (4πp0R2)X, where Xis a constant and γ = Cp/Cv=41/30. The value of Xis________.Correct answer is '2.05'. Can you explain this answer?
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A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R - a). For aRthe magnitude of the work done in the process is given by (4πp0R2)X, where Xis a constant and γ = Cp/Cv=41/30. The value of Xis________.Correct answer is '2.05'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R - a). For aRthe magnitude of the work done in the process is given by (4πp0R2)X, where Xis a constant and γ = Cp/Cv=41/30. The value of Xis________.Correct answer is '2.05'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R - a). For aRthe magnitude of the work done in the process is given by (4πp0R2)X, where Xis a constant and γ = Cp/Cv=41/30. The value of Xis________.Correct answer is '2.05'. Can you explain this answer?.
A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R - a). For aRthe magnitude of the work done in the process is given by (4πp0R2)X, where Xis a constant and γ = Cp/Cv=41/30. The value of Xis________.Correct answer is '2.05'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R - a). For aRthe magnitude of the work done in the process is given by (4πp0R2)X, where Xis a constant and γ = Cp/Cv=41/30. The value of Xis________.Correct answer is '2.05'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R - a). For aRthe magnitude of the work done in the process is given by (4πp0R2)X, where Xis a constant and γ = Cp/Cv=41/30. The value of Xis________.Correct answer is '2.05'. Can you explain this answer?.
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