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You decide to take a nice hot bath but discover that your thoughtless roommate has used up most of the hot water. You fill the tub with 270 kg of 30.0°C water and attempt to warm it further by pouring in 5.00 kg of boiling water from the stove.
(a) Is this a reversible or an irreversible process? Use physical reasoning to explain.
(b) Calculate the final temperature of the bath water.
(c) Calculate the net change in entropy of the system (bath water + boiling water), assuming no heat exchange with the air or the tub itself.

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  1. a) Mixing high and low temperature is an irreversible process. You cannot separate the equilibrated mixture into high and low temperature without performing work. Could you run the mixing process backwards? No way.

    b) Set the heat loss by the warm water equal to the heat gained by the cold water, and solve for final T.

    c) Entropy gain =
    Q/Tfinal - Q/t1 - Q/T2.

    Get Q (the heat transfer) from part (b)

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