Question

A sample of water is heated at a constant pressure of one atmosphere. Initially, the sample is ice at 260 K, and at the end the sample consists of steam at 400 K. In which of the following 5K temperature intervals would there be the greatest increase in the entropy of the sample? Multiple Choice
a. from 360 K to 365 K
b. from 260 K to 265 K
c. from 370 K to 375 K
d. from 395 K to 400 K
e. from 275 K to 280 K

Answer 1

In 370 K to 375 K temperature intervals of 5 K, would be the greatest increase in the entropy of the sample.

Option: C

Explanation:

Because the largest difference in molar entropy occurs when a condensed phase (solid/liquid) transforms to the gas phase. Then change in entropy is equal to heat transfer divided by temperature: $\Delta \mathrm{S}=\frac{\Delta Q}{\mathrm{m} T}$.

According to given ice sample at 260 K, when this solid sample start converting into liquid sample it will gain positive temperature and steam will take place near 373 K (273 K ice temperature + $100^{\circ} \mathrm{C}$ temperature of boiling water). Therefore it’s very obvious that greatest increase in entropy will occur during 370 K – 375 K.