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Two systems with heat capacities 100cal/gm-K and 200cal/gm-K interact thermally and come to a common temperature 400K. If the initial temperature of system 1 is 500K, what was the initial temperature of systems (in Kelvin) scale 
    Correct answer is '350'. Can you explain this answer?
    Verified Answer
    Two systems with heat capacities 100cal/gm-K and 200cal/gm-K interact ...
    Let initial temperature of system 2 is T2. According to conservation of energy, we know that heat released from one system is equal to the heat absorbed by the other system, i.e.
    C1 (Tf – T1 ) = C2 (T2 –Tf )

    = –50+400
    T2 = 350K
    The correct answer is: 350
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    Most Upvoted Answer
    Two systems with heat capacities 100cal/gm-K and 200cal/gm-K interact ...
    Given Information:
    - Heat capacity of system 1 (C1) = 100 cal/gm-K
    - Heat capacity of system 2 (C2) = 200 cal/gm-K
    - Initial temperature of system 1 (T1) = 500 K
    - Common temperature of both systems (Tf) = 400 K

    Calculating the final temperature of the mixture:
    When two systems interact thermally and reach a common temperature, the heat lost by one system is equal to the heat gained by the other system. This can be expressed using the formula:

    Q1 = -Q2

    where Q1 is the heat lost by system 1 and Q2 is the heat gained by system 2.

    The heat lost by system 1 can be calculated using the formula:

    Q1 = C1 * (T1 - Tf)

    The heat gained by system 2 can be calculated using the formula:

    Q2 = C2 * (Tf - T2)

    Since the heat lost by system 1 is equal to the heat gained by system 2, we can equate the two equations:

    C1 * (T1 - Tf) = C2 * (Tf - T2)

    Substituting the given values:

    100 * (500 - 400) = 200 * (400 - T2)

    Simplifying the equation:

    10000 = 80000 - 200T2
    200T2 = 70000
    T2 = 70000/200
    T2 = 350 K

    Conclusion:
    The initial temperature of system 2 (T2) was 350 K.
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    Two systems with heat capacities 100cal/gm-K and 200cal/gm-K interact thermally and come to a common temperature 400K. If the initial temperature of system 1 is 500K, what was the initial temperature of systems (in Kelvin) scaleCorrect answer is '350'. Can you explain this answer?
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