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 $1\space K$.

Equation:

$$ \LARGE{Q = mc\Delta{\theta}} $$

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

$m$ - Mass of substance (kg)

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

$\Delta{\theta}$ - Temperature change in $K$ or $^{\circ} C$

Why are the values for Specific Heat Capacity the same for either units? ($\cdots K^{-1}$ or $\cdots^{\circ}C^{-1}$)

Specific Heat Capacity relies on the change in temperature ($\Delta{\theta}$). 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 $J\space kg^{-1}K^{-1}$ or $J\space kg^{-1}\ ^{\circ}C^{-1}$.

Starter Questions

$Q1.$ A $1.5\space kg$ sample of a substance with specific heat capacity of $4200 J\space kg^{-1}K^{-1}$ is heated up by $32^{\circ}C$. Calculate the change in internal energy of the substance.

$Q2.$ A scientist wants to determine the specific heat capacity of substance Q. They take one 1kg sample of Q, and record that $37kJ$ 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.

$Q3.$ Find the increase in temperature, in Kelvin, that a 1kg sample of a substance with a specific heat capacity of $5000 J\space kg^{-1}K^{-1}$ when $25kJ$ of work is done on the substance.