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You drop a 285-g silver figure of a polar bear into the 241-g aluminum cup of...

You drop a 285-g silver figure of a polar bear into the 241-g aluminum cup of a well-insulated calorimeter containing 263 g of liquid water at 23.9°C. The bear\'s initial temperature is 95.9°C. What is the final temperature of the water, cup, and bear when they reach thermal equilibrium? The specific heats of silver, aluminum, and liquid water are, respectively, 234 J/(kg·K), 910 J/(kg·K), and 4190 J/(kg·K).

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Answer #1

According to the concept of the thermal properticies of the matter

m1s1(T1-T3)=(m2s2+m2s3)(T3-T2)

Given that

mass m1=0.285 kg

mass m2=0.241 kg

mass m3=0.263 kg

temperature T1=95.9 +273=369.9 k

temperature T2=23.9+273=296.9 K

now we find the finial temperature

0.285*234*(369.9-T3)=(0.241*910+0.263*4190)(T3-296.9)

66.69(369.9-T3)=1321.3*(T3-296.9)

369.9-T3=19.8[T3-296.9]

369.9-T3=19.8T3-5878.62

369.9+5878.62=(19.8+1)T3

T3=6248.52/20.8=300.41 K

the finial temperature T3=300.41 K=(300.41-273)=27.4 C

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