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When a block of cold carbon steel touches a hot aluminium block in an insulated chamber,both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures.determine the equilibrium temperature if the aluminium block has a mass of 10kg and an initial temperature of 380degree celsius and the carbon steel block has a mass of 25kg and an initial temperature of 10 degree celsius?
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When a block of cold carbon steel touches a hot aluminium block in an ...
Explanation:
When two objects at different temperatures are brought into contact with each other, heat flows from the hotter object to the colder object until both objects reach thermal equilibrium, i.e., the same temperature.
Calculating the final temperature:
We can use the principle of conservation of energy to calculate the final temperature of the two blocks. The total heat lost by the hot aluminium block is equal to the total heat gained by the cold carbon steel block.
Heat lost by aluminium block = Heat gained by carbon steel block
Q(aluminium) = Q(steel)
The heat lost or gained by an object can be calculated using the following formula:
Q = m * c * ΔT
where Q is the heat lost or gained, m is the mass of the object, c is the specific heat capacity of the object, and ΔT is the change in temperature.
Calculating the heat lost by the aluminium block:
Q(aluminium) = m(aluminium) * c(aluminium) * ΔT(aluminium)
Here, m(aluminium) = 10 kg (mass of aluminium block)
c(aluminium) = 0.9 kJ/kg°C (specific heat capacity of aluminium)
ΔT(aluminium) = Tf - Ti = Tf - 380°C (change in temperature)
Calculating the heat gained by the carbon steel block:
Q(steel) = m(steel) * c(steel) * ΔT(steel)
Here, m(steel) = 25 kg (mass of carbon steel block)
c(steel) = 0.46 kJ/kg°C (specific heat capacity of carbon steel)
ΔT(steel) = Tf - Ti = Tf - 10°C (change in temperature)
Equating the heat lost and gained:
Q(aluminium) = Q(steel)
m(aluminium) * c(aluminium) * ΔT(aluminium) = m(steel) * c(steel) * ΔT(steel)
Substituting the values, we get:
10 * 0.9 * (Tf - 380) = 25 * 0.46 * (Tf - 10)
Simplifying the equation, we get:
9Tf - 3420 = 11.5Tf - 287.5
2.5Tf = 3132.5
Tf = 1253°C
Therefore, the equilibrium temperature of the two blocks is 1253°C.
Conclusion:
In an insulated chamber, when a block of cold carbon steel touches a hot aluminium block, both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures. We can use the principle of conservation of energy to calculate the final temperature of the two blocks. In this case, the equilibrium temperature is calculated to be 1253°C.
When two objects at different temperatures are brought into contact with each other, heat flows from the hotter object to the colder object until both objects reach thermal equilibrium, i.e., the same temperature.
Calculating the final temperature:
We can use the principle of conservation of energy to calculate the final temperature of the two blocks. The total heat lost by the hot aluminium block is equal to the total heat gained by the cold carbon steel block.
Heat lost by aluminium block = Heat gained by carbon steel block
Q(aluminium) = Q(steel)
The heat lost or gained by an object can be calculated using the following formula:
Q = m * c * ΔT
where Q is the heat lost or gained, m is the mass of the object, c is the specific heat capacity of the object, and ΔT is the change in temperature.
Calculating the heat lost by the aluminium block:
Q(aluminium) = m(aluminium) * c(aluminium) * ΔT(aluminium)
Here, m(aluminium) = 10 kg (mass of aluminium block)
c(aluminium) = 0.9 kJ/kg°C (specific heat capacity of aluminium)
ΔT(aluminium) = Tf - Ti = Tf - 380°C (change in temperature)
Calculating the heat gained by the carbon steel block:
Q(steel) = m(steel) * c(steel) * ΔT(steel)
Here, m(steel) = 25 kg (mass of carbon steel block)
c(steel) = 0.46 kJ/kg°C (specific heat capacity of carbon steel)
ΔT(steel) = Tf - Ti = Tf - 10°C (change in temperature)
Equating the heat lost and gained:
Q(aluminium) = Q(steel)
m(aluminium) * c(aluminium) * ΔT(aluminium) = m(steel) * c(steel) * ΔT(steel)
Substituting the values, we get:
10 * 0.9 * (Tf - 380) = 25 * 0.46 * (Tf - 10)
Simplifying the equation, we get:
9Tf - 3420 = 11.5Tf - 287.5
2.5Tf = 3132.5
Tf = 1253°C
Therefore, the equilibrium temperature of the two blocks is 1253°C.
Conclusion:
In an insulated chamber, when a block of cold carbon steel touches a hot aluminium block, both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures. We can use the principle of conservation of energy to calculate the final temperature of the two blocks. In this case, the equilibrium temperature is calculated to be 1253°C.
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When a block of cold carbon steel touches a hot aluminium block in an insulated chamber,both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures.determine the equilibrium temperature if the aluminium block has a mass of 10kg and an initial temperature of 380degree celsius and the carbon steel block has a mass of 25kg and an initial temperature of 10 degree celsius?
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When a block of cold carbon steel touches a hot aluminium block in an insulated chamber,both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures.determine the equilibrium temperature if the aluminium block has a mass of 10kg and an initial temperature of 380degree celsius and the carbon steel block has a mass of 25kg and an initial temperature of 10 degree celsius? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about When a block of cold carbon steel touches a hot aluminium block in an insulated chamber,both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures.determine the equilibrium temperature if the aluminium block has a mass of 10kg and an initial temperature of 380degree celsius and the carbon steel block has a mass of 25kg and an initial temperature of 10 degree celsius? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a block of cold carbon steel touches a hot aluminium block in an insulated chamber,both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures.determine the equilibrium temperature if the aluminium block has a mass of 10kg and an initial temperature of 380degree celsius and the carbon steel block has a mass of 25kg and an initial temperature of 10 degree celsius?.
When a block of cold carbon steel touches a hot aluminium block in an insulated chamber,both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures.determine the equilibrium temperature if the aluminium block has a mass of 10kg and an initial temperature of 380degree celsius and the carbon steel block has a mass of 25kg and an initial temperature of 10 degree celsius? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about When a block of cold carbon steel touches a hot aluminium block in an insulated chamber,both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures.determine the equilibrium temperature if the aluminium block has a mass of 10kg and an initial temperature of 380degree celsius and the carbon steel block has a mass of 25kg and an initial temperature of 10 degree celsius? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a block of cold carbon steel touches a hot aluminium block in an insulated chamber,both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures.determine the equilibrium temperature if the aluminium block has a mass of 10kg and an initial temperature of 380degree celsius and the carbon steel block has a mass of 25kg and an initial temperature of 10 degree celsius?.
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When a block of cold carbon steel touches a hot aluminium block in an insulated chamber,both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures.determine the equilibrium temperature if the aluminium block has a mass of 10kg and an initial temperature of 380degree celsius and the carbon steel block has a mass of 25kg and an initial temperature of 10 degree celsius?, a detailed solution for When a block of cold carbon steel touches a hot aluminium block in an insulated chamber,both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures.determine the equilibrium temperature if the aluminium block has a mass of 10kg and an initial temperature of 380degree celsius and the carbon steel block has a mass of 25kg and an initial temperature of 10 degree celsius? has been provided alongside types of When a block of cold carbon steel touches a hot aluminium block in an insulated chamber,both blocks eventually reach thermal equilibrium at a temperature between their initial temperatures.determine the equilibrium temperature if the aluminium block has a mass of 10kg and an initial temperature of 380degree celsius and the carbon steel block has a mass of 25kg and an initial temperature of 10 degree celsius? theory, EduRev gives you an
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