Question

A 100 kg sample of a metal is cooled from 90°C to 20°C by removing 20 kcal of heat. Calculate the specific heat capacity of the metal.

Answer 1

Given:

The mass of the sample is,

`\begin{gathered} m=100\text{ kg} \\ =100*10^3\text{ g} \end{gathered}`

The temperature changes from

`90\text{ }\degree C\text{ to 20 }\degree C`

The heat rejected is,

`\begin{gathered} H=20\text{ kcal} \\ =20*10^3\text{ cal} \end{gathered}`

To find:

The specific heat capacity of the metal

Step-by-step explanation:

Let the specific heat capacity is 'c.'

The amount of heat rejected by the metal is,

`H=mc\Delta t`

Here, the temperature change is

`\begin{gathered} \Delta t=90-20 \\ =70\text{ }\degree C \end{gathered}`

Substituting the values we get,

`\begin{gathered} 20*10^3=100*10^3* c*70 \\ c=(20*10^3)/(100*10^3*70) \\ c=2.86*10^(-3)\text{ cal/g.}\degree C \end{gathered}`

Hence, the specific heat capacity is,

`2.86*10^(-3)\text{ cal/g.}\degree C`