Specific heat capacity

In a nutshell

Heating a material may cause its temperature to increase. The amount of heat needed to increase a substance's temperature depends on its specific heat capacity.

Equations

Word Equation	Symbol Equation
$thermal \space energy \space transferred = mass \,\times\, specific \,\, heat \,\, capacity \, \times change \,\, in \,\, temperature$	$E=m\times c\times \Delta T$

Variable Definitions

Quantity Name	Symbol	Unit Name	Unit
$thermal \space energy \space transferred$	$E$	$joule$	$J$
$mass$	$m$	$kilogram$	$kg$
$specific \,\, heat \,\, capacity$	$c$	$joule \,\, per \,\, kilogram \,\, celsius$	$J/(kg^{\,o}C)$
$change \,\, in \,\, temperature$	$\Delta T$	$degree\,\, celsius$	$^oC$

Specific heat capacity

Definition

Specific heat capacity is the amount of heat needed to change the temperature of $1kg$ of a substance by $1^oC$ .

Particles in a system have kinetic energy due to their motion. Transferring heat to/from a system either changes its temperature or changes its state.

Note: A system is a portion of the universe that has been chosen for studying the changes that take place within in as a response to varying conditions.

When the temperature of a system increases(decreases), the thermal energy transferred to(from) the system makes the particles move faster(slower), which increases(decreases) their kinetic energy.

How much the temperature of a system increases(decreases) when thermal energy is transferred to(from) it depends on the substance being heated(cooled), the amount of heat, and how much mass there is to heat(cool).

The equation linking thermal energy transferred to the change in temperature is:

$thermal \space energy \space transferred = mass \space \times\space specific \space heat \space capacity \space \times change \space in \space temperature$

$E=m\,\times c\,\times \Delta T$

where the variables are defined above.

Example

The specific heat capacity of copper is $389 J/(kg^{\,o}C)$ . How much heat is required to increase the temperature of $20g$ of copper by $15^{\,o}C$ ?

Write down the relevant information provided in the question (converting to base units where appropriate):

$c=389\,J/(kg^{\,o}C) \newline m=20\,g=0.02\,kg \newline \Delta T = 15^{\,o}C$

Write down the relevant formula:

$E=m\,\times\,c\,\times\,\Delta T$

Substitute the relevant information into the correct formula:

$E=0.02\,\times\,389\,\times\,15=\underline{117\,J}$

So $\underline {117\, J}$ of heat is required to increase increase the temperature of $20\,g$ of copper by $15^{\,o}C$ .