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.

$q_1=-q_2$

$m_1\times c_1\times (T_f-T_1)=-m_2\times c_2\times (T_f-T_2)$

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

$97g\times c_1\times (28.9-100)^oC=-122g\times 4.18J/g^oC\times (28.9-20.0)^oC$

$c_1=0.658J/g^oC$

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