Define specific heat capacity in terms of thermal energy, mass and temperature change.
An aluminium block has a volume of $3.612 \times 10^{-3}\,\text{m}^3$ at $0\,^\circ\text{C}$. Aluminium has a density of $2.700 \times 10^3\,\text{kg m}^{-3}$ at $0\,^\circ\text{C}$. It has a density of $2.620 \times 10^3\,\text{kg m}^{-3}$ at $500\,^\circ\text{C}$. The block is heated from $0\,^\circ\text{C}$ to $500\,^\circ\text{C}$ under an atmospheric pressure of $1.01 \times 10^5\,\text{Pa}$. Its internal energy increases by $4.38\,\text{MJ}$.
Calculate the mass of the block from the data provided.
Show that the volume of the block at $500\,^\circ\text{C}$ is $3.722 \times 10^{-3}\,\text{m}^3$.
Use the information in (b)(ii) to determine the magnitude of the work done on the block as its temperature rises from $0\,^\circ\text{C}$ to $500\,^\circ\text{C}$.
Explain whether the work done on the block has a positive or negative sign.
Use the first law of thermodynamics to find, to three significant figures, a value for the specific heat capacity of aluminium. Explain your working. Give a unit with your answer.
Without further calculation, suggest with a reason how doubling the pressure in (b) is likely to change the answer in (b)(v).