In the production of iron in a blast furnace, compressed air and oxygen are driven into molten iron ore. Engineers must understand the thermodynamic aspects of each part of the process so that it can be optimized, including changes to the entropy of oxygen. In one experiment, 1.00 mol O₂(g) was compressed suddenly (and irreversibly) from 5.00 L to 1.00 L by driving in a piston, and in the process its temperature was increased from 20.0°C to 25.2°C. What is the change in entropy of the gas?

ANTICIPATE The entropy will decrease when a gas is compressed, but increase when its temperature rises. Because the temperature rise is small, you should expect an overall decrease, but you must do the calculation to be sure.

PLAN Because entropy is a state function, calculate the change in entropy by choosing a reversible path that results in the same final state. In this case, two variables are changed, so consider the following two hypothetical steps:

Step 1 Reversible isothermal compression at the initial temperature from the initial volume to the final volume (use Eq. 2).

Step 2 An increase in temperature of the gas at constant final volume to the final temperature (use C_V in Eq. 4).

What should you assume? Assume that oxygen is an ideal gas and that C_V is constant over the temperature range.

Transcribed Image Text:

V₂ AS nR In- = V₁ (2)