Question

The Starship Enterprise is caught in a time warp and Spock is forced to use the primitive techniques of the 20th century to determine the specific heat capacity of an unknown mineral. The 307-g sample was heated to 98.7°C and placed into a calorimeter containing 72.4 g of water at 23.6°C. The heat capacity of the calorimeter was 15.7 J/K. The final temperature in the calorimeter was 32.4°C. What is the specific heat capacity of the mineral?

Answer 1

Answer : The specific heat capacity of the mineral is $0.131J/g^oC$

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 unknown mineral = ?

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

$m_1$ = mass of unknown mineral = 307 g

$m_2$ = mass of water = 72.4 g

$T_f$ = final temperature of calorimeter = $32.4^oC$

$T_1$ = initial temperature of unknown mineral = $98.7^oC$

$T_2$ = initial temperature of water = $23.6^oC$

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

$307g\times c_1\times (32.4-98.7)^oC=-72.4g\times 4.18J/g^oC\times (32.4-23.6)^oC$

$c_1=0.131J/g^oC$

Therefore, the specific heat capacity of the mineral is $0.131J/g^oC$