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Two thermally isolated systems have heat capacities which vary as Cv = βT2 (where β > 0). Initially one system is at 300 K and the other at 600 K. The systems are then brought into thermal contact and the combined system is allowed to reach thermal equilibrium. Then calculate the final temperature (in Kelvin) of the combined system.
Correct answer is '495'. Can you explain this answer?
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Two thermally isolated systems have heat capacities which vary as Cv =...
Let the final temperature of combined system is T
Heat lost = Heat gained
T3 - 6003 = 3003 - T3
2T3 = 3003 + 6003
2T3 = 243 x 106
T = 495 K
Heat lost = Heat gained
T3 - 6003 = 3003 - T3
2T3 = 3003 + 6003
2T3 = 243 x 106
T = 495 K
Most Upvoted Answer
Two thermally isolated systems have heat capacities which vary as Cv =...
Cv = Cv0 + αT
where Cv is the heat capacity, Cv0 is the initial heat capacity at T=0, α is the coefficient of thermal expansion, and T is the temperature.
If the two systems are in thermal equilibrium, the total heat capacity is given by:
Cv_total = Cv1 + Cv2
Substituting the expressions for Cv1 and Cv2, we have:
Cv_total = (Cv1_0 + α1T) + (Cv2_0 + α2T)
Simplifying, we get:
Cv_total = (Cv1_0 + Cv2_0) + (α1 + α2)T
Therefore, the total heat capacity of the two systems is given by:
Cv_total = Cv_total_0 + α_total T
where Cv_total_0 = Cv1_0 + Cv2_0 is the initial total heat capacity and α_total = α1 + α2 is the total coefficient of thermal expansion.
where Cv is the heat capacity, Cv0 is the initial heat capacity at T=0, α is the coefficient of thermal expansion, and T is the temperature.
If the two systems are in thermal equilibrium, the total heat capacity is given by:
Cv_total = Cv1 + Cv2
Substituting the expressions for Cv1 and Cv2, we have:
Cv_total = (Cv1_0 + α1T) + (Cv2_0 + α2T)
Simplifying, we get:
Cv_total = (Cv1_0 + Cv2_0) + (α1 + α2)T
Therefore, the total heat capacity of the two systems is given by:
Cv_total = Cv_total_0 + α_total T
where Cv_total_0 = Cv1_0 + Cv2_0 is the initial total heat capacity and α_total = α1 + α2 is the total coefficient of thermal expansion.
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Two thermally isolated systems have heat capacities which vary as Cv = βT2 (where β > 0). Initially one system is at 300 K and the other at 600 K. The systems are then brought into thermal contact and the combined system is allowed to reach thermal equilibrium. Then calculate the final temperature (in Kelvin) of the combined system.Correct answer is '495'. Can you explain this answer?
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Two thermally isolated systems have heat capacities which vary as Cv = βT2 (where β > 0). Initially one system is at 300 K and the other at 600 K. The systems are then brought into thermal contact and the combined system is allowed to reach thermal equilibrium. Then calculate the final temperature (in Kelvin) of the combined system.Correct answer is '495'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Two thermally isolated systems have heat capacities which vary as Cv = βT2 (where β > 0). Initially one system is at 300 K and the other at 600 K. The systems are then brought into thermal contact and the combined system is allowed to reach thermal equilibrium. Then calculate the final temperature (in Kelvin) of the combined system.Correct answer is '495'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two thermally isolated systems have heat capacities which vary as Cv = βT2 (where β > 0). Initially one system is at 300 K and the other at 600 K. The systems are then brought into thermal contact and the combined system is allowed to reach thermal equilibrium. Then calculate the final temperature (in Kelvin) of the combined system.Correct answer is '495'. Can you explain this answer?.
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