453 g of water at 54°C &111 g of glycerin at 15°C are pouredinto a 146 g copper

Question

453 g of water at 54°C &111 g of glycerin at 15°C are pouredinto a 146 g copper cup at 14°C.Assuming these three make up a closed (or isolated) system,determine the final temperature of the system. The specific heat ofwater is 4186 J/kg·°C. The specific heat of glycerin is2410 J/kg·°C. The specific heat of copper is 387J/kg·°C.
°C

Got this one wrong 453 g of water at 54°C &111 g of glycerin at 15°C are pouredinto a 146 g copper cup at 14°C.Assuming these three make up a closed (or isolated) system,determine the final temperature of the system. The specific heat ofwater is 4186 J/kg·°C. The specific heat of glycerin is2410 J/kg·°C. The specific heat of copper is 387J/kg·°C.
°C

Got this one wrong

Explanation / Answer

mass of water m = 453 g = 0.453 kg initial temp of water t = 54 oC mass of glycerin m ' = 111 g =0.111 kg initial temp of glycerin t ' = 15 oC mass of copper m " = 146 g = 0.146 kg initial temp of copper t " = 14 oC The specific heat of water c = 4186J/kg·°C The specific heat of glycerin c ' = 2410J/kg·°C The specific heat of copper c " = 387J/kg·°C. Heat lost by water = heat gain by glycerin + copper    mc ( 54-T ) = m ' c ' ( T -15) + m" c" ( T -14) 102397.932 - 1896.258 T =267.51 T - 4012.65 +56.502 T - 791.028 107201.61 =2220.27 T final temperature T = 48.28 oC

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