Question

A coin dealer, offered a rare silver coin, suspected that it might be a counterfeit nickel copy. The dealer heated the coin, which weighed 16.5 g to 100°C in boiling water and then dropped the hot coin into 22.5 g of water at T = 15.5°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 )

Answer 1

Answer : The final temperature of the water will be,
`18.8^oC`

Explanation :

In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.

`q_1=-q_2`

`m_1* c_1* (T_f-T_1)=-m_2* c_2* (T_f-T_2)`

where,

`c_1` = specific heat of silver =
`0.233J/g^oC`

`c_2` = specific heat of water =
`4.18J/g^oC`

`m_1` = mass of silver coin = 16.5 g

`m_2` = mass of water = 22.5 g

`T_f` = final temperature of water = ?

`T_1` = initial temperature of silver coin =
`100^oC`

`T_2` = initial temperature of water =
`15.5^oC`

Now put all the given values in the above formula, we get

`16.5g* 0.233J/g^oC* (T_f-100)^oC=-22.5g* 4.18J/g^oC* (T_f-15.5)^oC`

`T_f=18.8^oC`

Therefore, the final temperature of the water will be,
`18.8^oC`