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A coin dealer, offered a rare silver coin, suspected that it might be a counterfeit nickel...

A coin dealer, offered a rare silver coin, suspected that it might be a counterfeit nickel copy. The dealer heated the coin, which weighed 14.0 g to 100°C in boiling water and then dropped the hot coin into 25.0 g of water at T = 16.5°C in an insulated coffee-cup, and measured the rise in temperature. If the coin was really made of silver, what would the final temperature of the water be (in °C)? (for nickel, s = 0.445 J/g°C; for silver, s = 0.233 J/g°C )
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Answer #1

Let final temperature of system is t ℃ .

Heat lost by silver coin = m.s.∆T = 14.0g × 0.233J/g.℃ ×( 100-t)℃

Heat gained by water = m.s.∆T = 25.0g×4.184J/g.℃ ×(t - 16.5)℃

Heat gained by water = heat lost by silver coin

14.0×0.233×(100-t) = 25.0×4.184×(t-16.5)

326.2 - 3.262×t = 104.6×t -1725.9

t = 2052.1/107.862 = 19.02524

If the coin was really made of silver , the final temperature of water should be 19.0 ℃ (Answer)

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