Thermal Expansion

Solution

To estimate the percent difference in the density of iron at STP and under extreme conditions (2000°C, 5000 atm), we analyze the effects of thermal expansion and compression.

Step 1: Density at STP

The density of iron at STP (0°C, 1 atm) is:

Step 2: Thermal Expansion Effect

The coefficient of volume expansion for iron is derived from its linear expansion coefficient ($\alpha =12\times {10}^{-6}{\text{°C}}^{-1}$):

The temperature change is $\mathrm{\Delta }T=2000\text{°C}$. The fractional volume increase is:

Since density is inversely proportional to volume:

Step 3: Compression Effect

The bulk modulus $K=90\times {10}^9{\text{N/m}}^2$. The pressure increase is:

The fractional volume decrease is:

This corresponds to a density increase:

Step 4: Net Density Change

Combining the effects:

The percent difference in density is:

Footnotes