Specific Heat Capacity

Specific Heat Capacity - The amount of energy needed to increase the temperature of 1kg of a (pure) substance by $1^{\circ} C$ or $1 K$ .

Equation:

$Q = m c Δ θ$

Where, $Q$ - Change in energy ( $J$ )

$m$ - Mass of substance (kg)

$c$ - Specific Heat Capacity ( $J k g^{- 1} K^{- 1}$ or $J k g^{- 1}^{\circ} C^{- 1}$ )

$Δ θ$ - Temperature change in $K$ or $^{\circ} C$

Why are the values for Specific Heat Capacity the same for either units? (

\dots K^{- 1}

\dots^{\circ} C^{- 1}

)

Specific Heat Capacity relies on the change in temperature ( $Δ θ$ ). Since a change of $1^{\circ} C$ is the same as a change of $1 K$ , the magnitude of the specific heat capacity is same whether written with units $J k g^{- 1} K^{- 1}$ or $J k g^{- 1}^{\circ} C^{- 1}$ .

Starter Questions

Q 1.

1.5 k g

sample of a substance with specific heat capacity of

4200 J k g^{- 1} K^{- 1}

is heated up by

32^{\circ} C

. Calculate the change in internal energy of the substance.

Q 2.

A scientist wants to determine the specific heat capacity of substance Q. They take one 1kg sample of Q, and record that

37 k J

of work has been done to heat the sample up by

3^{\circ} C

. a) Work out the specific heat capacity of Q. b) State how the scientist could improve the accuracy of his result.

The scientist should repeat the experiment at least 2 more times to get an average result for the specific heat capacity.

Q 3.

Find the increase in temperature, in Kelvin, that a 1kg sample of a substance with a specific heat capacity of

5000 J k g^{- 1} K^{- 1}

when

25 k J

of work is done on the substance.