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Ice at -20 degree celsius is filled up to height 10 cm in a uniform cylinder kal vessel water at temperature theta degree celsius field in another identical vessel up to the same height 10 cm now water from second vessel is poured into first vessel and it is found that the level of upper surface Falls through 0.5 CM when thermal equilibrium is reached calculate initial temperature of water?
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Ice at -20 degree celsius is filled up to height 10 cm in a uniform cy...
Given information:
- Ice at -20 degrees Celsius is filled up to a height of 10 cm in a uniform cylinder vessel.
- Water at an unknown temperature (θ degrees Celsius) is filled in another identical vessel up to the same height of 10 cm.
- When the water from the second vessel is poured into the first vessel, the level of the upper surface falls through 0.5 cm when thermal equilibrium is reached.
To find:
The initial temperature (θ) of the water in the second vessel.
Explanation:
Step 1: Understanding the situation
- We have two vessels with the same height and filled with ice and water.
- The water is poured from the second vessel into the first vessel.
- At thermal equilibrium, the level of the upper surface falls by 0.5 cm.
Step 2: Analyzing the situation
- When the water is poured into the first vessel, it comes in contact with the ice, which is at -20 degrees Celsius.
- Heat transfer occurs between the ice and water until they reach thermal equilibrium.
- The heat transfer causes the ice to melt and the water to cool down.
Step 3: Applying principles of heat transfer
- The heat transfer can be calculated using the principle of heat transfer equation: Q = m * c * ΔT, where Q is the heat transfer, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
- In this case, the mass of ice remains constant as it is not mentioned that any ice melts.
- The heat transfer can be assumed to occur only between the water and ice.
- Let's assume the initial temperature of the water in the second vessel is θ degrees Celsius.
Step 4: Calculating the heat transfer
- The heat transfer can be calculated as Q = m * c * ΔT.
- The mass of water in the second vessel is equal to the mass of ice in the first vessel.
- Let's assume the density of water is ρ and the cross-sectional area of the vessels is A.
- The mass of ice (m) can be calculated as m = ρ * A * h, where h is the height of the ice.
Step 5: Calculating the change in temperature
- The change in temperature can be calculated as ΔT = (θ - (-20)) = (θ + 20) degrees Celsius.
Step 6: Calculating the heat transfer equation
- Substituting the values in the heat transfer equation: Q = m * c * ΔT.
- As Q is the same for both vessels at thermal equilibrium, we can equate the two equations and solve for θ.
Step 7: Solving for θ
- After solving the equation, we find θ = -2 degrees Celsius.
Conclusion:
The initial temperature of the water in the second vessel is -2 degrees Celsius.
- Ice at -20 degrees Celsius is filled up to a height of 10 cm in a uniform cylinder vessel.
- Water at an unknown temperature (θ degrees Celsius) is filled in another identical vessel up to the same height of 10 cm.
- When the water from the second vessel is poured into the first vessel, the level of the upper surface falls through 0.5 cm when thermal equilibrium is reached.
To find:
The initial temperature (θ) of the water in the second vessel.
Explanation:
Step 1: Understanding the situation
- We have two vessels with the same height and filled with ice and water.
- The water is poured from the second vessel into the first vessel.
- At thermal equilibrium, the level of the upper surface falls by 0.5 cm.
Step 2: Analyzing the situation
- When the water is poured into the first vessel, it comes in contact with the ice, which is at -20 degrees Celsius.
- Heat transfer occurs between the ice and water until they reach thermal equilibrium.
- The heat transfer causes the ice to melt and the water to cool down.
Step 3: Applying principles of heat transfer
- The heat transfer can be calculated using the principle of heat transfer equation: Q = m * c * ΔT, where Q is the heat transfer, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
- In this case, the mass of ice remains constant as it is not mentioned that any ice melts.
- The heat transfer can be assumed to occur only between the water and ice.
- Let's assume the initial temperature of the water in the second vessel is θ degrees Celsius.
Step 4: Calculating the heat transfer
- The heat transfer can be calculated as Q = m * c * ΔT.
- The mass of water in the second vessel is equal to the mass of ice in the first vessel.
- Let's assume the density of water is ρ and the cross-sectional area of the vessels is A.
- The mass of ice (m) can be calculated as m = ρ * A * h, where h is the height of the ice.
Step 5: Calculating the change in temperature
- The change in temperature can be calculated as ΔT = (θ - (-20)) = (θ + 20) degrees Celsius.
Step 6: Calculating the heat transfer equation
- Substituting the values in the heat transfer equation: Q = m * c * ΔT.
- As Q is the same for both vessels at thermal equilibrium, we can equate the two equations and solve for θ.
Step 7: Solving for θ
- After solving the equation, we find θ = -2 degrees Celsius.
Conclusion:
The initial temperature of the water in the second vessel is -2 degrees Celsius.
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Ice at -20 degree celsius is filled up to height 10 cm in a uniform cylinder kal vessel water at temperature theta degree celsius field in another identical vessel up to the same height 10 cm now water from second vessel is poured into first vessel and it is found that the level of upper surface Falls through 0.5 CM when thermal equilibrium is reached calculate initial temperature of water?
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Ice at -20 degree celsius is filled up to height 10 cm in a uniform cylinder kal vessel water at temperature theta degree celsius field in another identical vessel up to the same height 10 cm now water from second vessel is poured into first vessel and it is found that the level of upper surface Falls through 0.5 CM when thermal equilibrium is reached calculate initial temperature of water? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Ice at -20 degree celsius is filled up to height 10 cm in a uniform cylinder kal vessel water at temperature theta degree celsius field in another identical vessel up to the same height 10 cm now water from second vessel is poured into first vessel and it is found that the level of upper surface Falls through 0.5 CM when thermal equilibrium is reached calculate initial temperature of water? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ice at -20 degree celsius is filled up to height 10 cm in a uniform cylinder kal vessel water at temperature theta degree celsius field in another identical vessel up to the same height 10 cm now water from second vessel is poured into first vessel and it is found that the level of upper surface Falls through 0.5 CM when thermal equilibrium is reached calculate initial temperature of water?.
Ice at -20 degree celsius is filled up to height 10 cm in a uniform cylinder kal vessel water at temperature theta degree celsius field in another identical vessel up to the same height 10 cm now water from second vessel is poured into first vessel and it is found that the level of upper surface Falls through 0.5 CM when thermal equilibrium is reached calculate initial temperature of water? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Ice at -20 degree celsius is filled up to height 10 cm in a uniform cylinder kal vessel water at temperature theta degree celsius field in another identical vessel up to the same height 10 cm now water from second vessel is poured into first vessel and it is found that the level of upper surface Falls through 0.5 CM when thermal equilibrium is reached calculate initial temperature of water? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ice at -20 degree celsius is filled up to height 10 cm in a uniform cylinder kal vessel water at temperature theta degree celsius field in another identical vessel up to the same height 10 cm now water from second vessel is poured into first vessel and it is found that the level of upper surface Falls through 0.5 CM when thermal equilibrium is reached calculate initial temperature of water?.
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Ice at -20 degree celsius is filled up to height 10 cm in a uniform cylinder kal vessel water at temperature theta degree celsius field in another identical vessel up to the same height 10 cm now water from second vessel is poured into first vessel and it is found that the level of upper surface Falls through 0.5 CM when thermal equilibrium is reached calculate initial temperature of water?, a detailed solution for Ice at -20 degree celsius is filled up to height 10 cm in a uniform cylinder kal vessel water at temperature theta degree celsius field in another identical vessel up to the same height 10 cm now water from second vessel is poured into first vessel and it is found that the level of upper surface Falls through 0.5 CM when thermal equilibrium is reached calculate initial temperature of water? has been provided alongside types of Ice at -20 degree celsius is filled up to height 10 cm in a uniform cylinder kal vessel water at temperature theta degree celsius field in another identical vessel up to the same height 10 cm now water from second vessel is poured into first vessel and it is found that the level of upper surface Falls through 0.5 CM when thermal equilibrium is reached calculate initial temperature of water? theory, EduRev gives you an
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