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SERPSE$1021\mathrm{.}7\mathrm{.}0$P$\mathrm{.}022.$

A block made of cobalt with a mass of $0\mathrm{.}80$ kg is heated to $800C,$ then dropped into $7\mathrm{.}00$ kg of water at $11C.$ What is the total change in entropy $($in J$/$K$)$ of the block$-$water system, assuming no energy is lost by heat from this system to the surroundings? The specific heat of cobalt is $420\frac{J}{kg*K},$ and the specific heat of water is $4,186\frac{J}{kg*K}.($Hint: note that $dQ=mcdT.)$

First, consider conservation of energy. Using the specific heats, can you find the final equilibrium temperature of the combined system? Next consider the infinitesimal change in entropy $dS.$ How does it depend on $dQ$ and temperature? Note the expression given for $dQ$ in the hint. Can you write an infinitesimal expression for each object that can be integrated from the initial to final temperature? J$/$K

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