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A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,
- a)the liquid will overflow
- b)the level of the liquid will fall
- c)the level of the liquid will remain unchanged
- d)the level of liquid will rise or fall depending on the nature of the metal and of the liquid
Correct answer is option 'C'. Can you explain this answer?
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A metallic container is completely filled with a liquid. The coefficie...
× 10^-5 /°C and the coefficient of volume expansion of the liquid is 5.0 × 10^-4 /°C. If the temperature increases by 50°C, what will be the change in volume of the liquid and the change in height of the liquid level in the container?
We can use the formula for linear expansion:
ΔL = αLΔT
where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.
Since the container is completely filled with liquid, the change in height of the liquid level will be equal to the change in length of the container. Therefore:
Δh = ΔL = αLΔT
We can also use the formula for volume expansion:
ΔV = βVΔT
where ΔV is the change in volume, β is the coefficient of volume expansion, V is the original volume, and ΔT is the change in temperature.
Since the container is completely filled with liquid, the change in volume of the liquid will be equal to the change in volume of the container. Therefore:
ΔV = ΔV_container = βV_containerΔT
We can relate the change in volume of the container to the change in height of the liquid level using the formula for the volume of a cylinder:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Since the container is completely filled with liquid, the radius of the container will not change. Therefore:
V_container = πr^2h
Taking the derivative of both sides with respect to time, we get:
dV_container/dt = πr^2dh/dt
Since the container is not expanding or contracting, the change in volume of the container must be equal to the change in volume of the liquid. Therefore:
dV_container/dt = dV/dt = ΔV/Δt
Substituting into the previous equation, we get:
ΔV/Δt = πr^2dh/dt
We can now solve for Δh:
Δh = ΔV/πr^2Δt
Substituting the expressions for ΔV and Δt, we get:
Δh = (βV_containerΔT)/πr^2
Substituting the expressions for β and V_container, we get:
Δh = (5.0 × 10^-4 /°C) × (πr^2h) × (50°C) / πr^2
Simplifying, we get:
Δh = 0.025h
Therefore, the change in height of the liquid level in the container is 2.5% of the original height.
To find the change in volume of the liquid, we can use the expression for ΔV:
ΔV = βVΔT
Substituting the expressions for β and V, we get:
ΔV = (5.0 × 10^-4 /°C) × V × (50°C)
Substituting the expression for V in terms of h, we get:
ΔV = (5.0 × 10^-4 /°C) × πr^2h × (50°C)
Simplifying,
We can use the formula for linear expansion:
ΔL = αLΔT
where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.
Since the container is completely filled with liquid, the change in height of the liquid level will be equal to the change in length of the container. Therefore:
Δh = ΔL = αLΔT
We can also use the formula for volume expansion:
ΔV = βVΔT
where ΔV is the change in volume, β is the coefficient of volume expansion, V is the original volume, and ΔT is the change in temperature.
Since the container is completely filled with liquid, the change in volume of the liquid will be equal to the change in volume of the container. Therefore:
ΔV = ΔV_container = βV_containerΔT
We can relate the change in volume of the container to the change in height of the liquid level using the formula for the volume of a cylinder:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Since the container is completely filled with liquid, the radius of the container will not change. Therefore:
V_container = πr^2h
Taking the derivative of both sides with respect to time, we get:
dV_container/dt = πr^2dh/dt
Since the container is not expanding or contracting, the change in volume of the container must be equal to the change in volume of the liquid. Therefore:
dV_container/dt = dV/dt = ΔV/Δt
Substituting into the previous equation, we get:
ΔV/Δt = πr^2dh/dt
We can now solve for Δh:
Δh = ΔV/πr^2Δt
Substituting the expressions for ΔV and Δt, we get:
Δh = (βV_containerΔT)/πr^2
Substituting the expressions for β and V_container, we get:
Δh = (5.0 × 10^-4 /°C) × (πr^2h) × (50°C) / πr^2
Simplifying, we get:
Δh = 0.025h
Therefore, the change in height of the liquid level in the container is 2.5% of the original height.
To find the change in volume of the liquid, we can use the expression for ΔV:
ΔV = βVΔT
Substituting the expressions for β and V, we get:
ΔV = (5.0 × 10^-4 /°C) × V × (50°C)
Substituting the expression for V in terms of h, we get:
ΔV = (5.0 × 10^-4 /°C) × πr^2h × (50°C)
Simplifying,
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A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer?
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A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer?.
A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10-6 per °C. On heating the vessel,a)the liquid will overflowb)the level of the liquid will fallc)the level of the liquid will remain unchangedd)the level of liquid will rise or fall depending on the nature of the metal and of the liquidCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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