Question

You are trying to determine the specific heat of a metal. You heat the 97 g piece of metal to 100 °C and place it in a calorimeter with 122 g of water. The temperature of the water increases from 20.0 °C to 28.9 °C. What is the specific heat of the metal?

Answer 1

Answer : The specific heat of the metal is,
`0.658J/g^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 metal = ?

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

`m_1` = mass of metal = 97 g

`m_2` = mass of water = 122 g

`T_f` = final temperature of mixture =
`28.9^oC`

`T_1` = initial temperature of metal =
`100^oC`

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

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

`97g* c_1* (28.9-100)^oC=-122g* 4.18J/g^oC* (28.9-20.0)^oC`

`c_1=0.658J/g^oC`

Therefore, the specific heat of the metal is,
`0.658J/g^oC`