I\'m having a problem deciding if my way of thinking about thisproblem is accura

Question

I'm having a problem deciding if my way of thinking about thisproblem is accurate. It almost seems to obvious: A student investigating the specific heat of an unknown metalused a styrofaom cup as a calorimeter. She measured the mass ofwater, 50.2025 g; the mass of metal 56.0371 g; the initialtemperature of the water was 23.5 degrees celsius; the initialtemperature of the metal was 99.5 degrees celsius; and the finaltemp. of the water and metal was 27 degrees celsius. Calculate thespecific heat of the metal.
Is 27 degrees celsius the final temperature of the metal ordoes that heat somehow divide amongst water and metal? If itis the metals final temperature can I simply plug that figure intoan equation to find the specific heat? A student investigating the specific heat of an unknown metalused a styrofaom cup as a calorimeter. She measured the mass ofwater, 50.2025 g; the mass of metal 56.0371 g; the initialtemperature of the water was 23.5 degrees celsius; the initialtemperature of the metal was 99.5 degrees celsius; and the finaltemp. of the water and metal was 27 degrees celsius. Calculate thespecific heat of the metal.
Is 27 degrees celsius the final temperature of the metal ordoes that heat somehow divide amongst water and metal? If itis the metals final temperature can I simply plug that figure intoan equation to find the specific heat?

Explanation / Answer

mass of water m = 50.2025 g
the mass of metal M = 56.0371 g the initial temperature of the water t = 23.5 degrees celsius the initial temperature of the metal t ' = 99.5 degrees celsius and the final temp. of the water and metal T = 27 degrees celsius Let the specific heat of the metal be C then heat loss by metal = heat gainn by water            M Cdt = m c dt ' where dt = 99.5 - T           dt' = T - 23.5           c= specific heat of water = 4.186 J / g oC substitue values weget , 56.0371 * C * ( 99.5- 27 ) = 50.2025 * 4.186 * ( 27 - 23.5 )                                                                              from this specific heat of metal C = 0.18104 J / goC

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