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A closed hollow insulated cylinder is filled with gas at 0 celcius and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to 100 celcius.If the piston moves 5cm the length of the hollow cylinder is.? 1)13.65cm. 2)27.3cm. 3)38.6cm. 4)64.6cm?
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A closed hollow insulated cylinder is filled with gas at 0 celcius and...
Given Information:
- A closed, hollow, insulated cylinder
- Gas filled at 0 degrees Celsius
- Insulated piston in the middle
- Gas on one side of the piston is heated to 100 degrees Celsius
- Piston moves 5cm
To Find:
The length of the hollow cylinder
Approach:
1. Understand the concept of thermal expansion.
2. Apply the principle of thermal expansion to find the change in length.
3. Use the given information to calculate the length of the hollow cylinder.
Solution:
1. Thermal Expansion:
When a substance is heated, its particles gain energy and move more vigorously, causing the substance to expand. The change in length (∆L) of a solid due to a change in temperature (∆T) can be calculated using the formula:
∆L = α * L * ∆T
Where:
∆L = Change in length
α = Coefficient of linear expansion
L = Initial length
∆T = Change in temperature
2. Applying Thermal Expansion:
In this scenario, the gas on one side of the piston is heated, causing it to expand. The piston is free to move, so it will be pushed in the direction of the expanded gas. We need to find the change in length (∆L) of the hollow cylinder.
Let's assume the initial length of the hollow cylinder is L.
The gas on one side is heated from 0°C to 100°C, resulting in a change in temperature (∆T) of:
∆T = 100°C - 0°C = 100°C
We also know that the piston moves by 5cm (∆L).
Using the formula for thermal expansion, we can rewrite it as:
∆L = α * L * ∆T
Solving for α, we have:
α = ∆L / (L * ∆T)
Substituting the given values:
α = 5cm / (L * 100°C)
3. Calculating the Length of the Hollow Cylinder:
To find the length of the hollow cylinder, we need to know the coefficient of linear expansion (α) for the gas inside.
The coefficient of linear expansion varies for different gases. Assuming the gas inside the hollow cylinder is an ideal gas, we can use the coefficient of linear expansion for an ideal gas at constant pressure:
α = 1 / (273 + t)
Where t is the temperature in degrees Celsius.
Substituting this value of α into our equation:
1 / (273 + t) = 5cm / (L * 100°C)
Simplifying:
L * 100°C = 5cm * (273 + t)
L = (5cm * (273 + t)) / 100°C
L = (5cm * (273 + 100)) / 100°C
L = (5cm * 373) / 100°C
L = 18.65cm
Therefore, the length of the hollow cylinder is approximately 18.65cm.
Answer:
The length of the hollow cylinder is approximately 18.65cm.
- A closed, hollow, insulated cylinder
- Gas filled at 0 degrees Celsius
- Insulated piston in the middle
- Gas on one side of the piston is heated to 100 degrees Celsius
- Piston moves 5cm
To Find:
The length of the hollow cylinder
Approach:
1. Understand the concept of thermal expansion.
2. Apply the principle of thermal expansion to find the change in length.
3. Use the given information to calculate the length of the hollow cylinder.
Solution:
1. Thermal Expansion:
When a substance is heated, its particles gain energy and move more vigorously, causing the substance to expand. The change in length (∆L) of a solid due to a change in temperature (∆T) can be calculated using the formula:
∆L = α * L * ∆T
Where:
∆L = Change in length
α = Coefficient of linear expansion
L = Initial length
∆T = Change in temperature
2. Applying Thermal Expansion:
In this scenario, the gas on one side of the piston is heated, causing it to expand. The piston is free to move, so it will be pushed in the direction of the expanded gas. We need to find the change in length (∆L) of the hollow cylinder.
Let's assume the initial length of the hollow cylinder is L.
The gas on one side is heated from 0°C to 100°C, resulting in a change in temperature (∆T) of:
∆T = 100°C - 0°C = 100°C
We also know that the piston moves by 5cm (∆L).
Using the formula for thermal expansion, we can rewrite it as:
∆L = α * L * ∆T
Solving for α, we have:
α = ∆L / (L * ∆T)
Substituting the given values:
α = 5cm / (L * 100°C)
3. Calculating the Length of the Hollow Cylinder:
To find the length of the hollow cylinder, we need to know the coefficient of linear expansion (α) for the gas inside.
The coefficient of linear expansion varies for different gases. Assuming the gas inside the hollow cylinder is an ideal gas, we can use the coefficient of linear expansion for an ideal gas at constant pressure:
α = 1 / (273 + t)
Where t is the temperature in degrees Celsius.
Substituting this value of α into our equation:
1 / (273 + t) = 5cm / (L * 100°C)
Simplifying:
L * 100°C = 5cm * (273 + t)
L = (5cm * (273 + t)) / 100°C
L = (5cm * (273 + 100)) / 100°C
L = (5cm * 373) / 100°C
L = 18.65cm
Therefore, the length of the hollow cylinder is approximately 18.65cm.
Answer:
The length of the hollow cylinder is approximately 18.65cm.
Community Answer
A closed hollow insulated cylinder is filled with gas at 0 celcius and...
38.6cm
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A closed hollow insulated cylinder is filled with gas at 0 celcius and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to 100 celcius.If the piston moves 5cm the length of the hollow cylinder is.? 1)13.65cm. 2)27.3cm. 3)38.6cm. 4)64.6cm?
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A closed hollow insulated cylinder is filled with gas at 0 celcius and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to 100 celcius.If the piston moves 5cm the length of the hollow cylinder is.? 1)13.65cm. 2)27.3cm. 3)38.6cm. 4)64.6cm? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A closed hollow insulated cylinder is filled with gas at 0 celcius and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to 100 celcius.If the piston moves 5cm the length of the hollow cylinder is.? 1)13.65cm. 2)27.3cm. 3)38.6cm. 4)64.6cm? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A closed hollow insulated cylinder is filled with gas at 0 celcius and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to 100 celcius.If the piston moves 5cm the length of the hollow cylinder is.? 1)13.65cm. 2)27.3cm. 3)38.6cm. 4)64.6cm?.
A closed hollow insulated cylinder is filled with gas at 0 celcius and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to 100 celcius.If the piston moves 5cm the length of the hollow cylinder is.? 1)13.65cm. 2)27.3cm. 3)38.6cm. 4)64.6cm? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A closed hollow insulated cylinder is filled with gas at 0 celcius and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to 100 celcius.If the piston moves 5cm the length of the hollow cylinder is.? 1)13.65cm. 2)27.3cm. 3)38.6cm. 4)64.6cm? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A closed hollow insulated cylinder is filled with gas at 0 celcius and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to 100 celcius.If the piston moves 5cm the length of the hollow cylinder is.? 1)13.65cm. 2)27.3cm. 3)38.6cm. 4)64.6cm?.
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