Choose which species in the following pairs have the greater

Choose which species in the following pairs have the greater U, and the greater S: a. 5 grams of Fe at 20 degree C, 1 atm; OR 10 grams of Fe at 20 degree C, 1 atm. b. 2 grams of water at 25 degree C, 1 atm; OR 2 grams of water at 25 degree C, 20 torr. c. 2 grams of benzene at 25 degree C, 1 bar; OR 2 grams of benzene at 40 degree C, 1 bar d. 2 grams of metal M at 300 degree K and 1 bar AND 2 grams of M at 310 degree K and 1 bar; OR 4 grams of M at 305 degree K and 1 bar e. One mole of ideal gas at 273 degree K and 1 bar; OR one mole of ideal gas at 273 degree K and 10 bar

Solution

the expression for the internal energy is,

U = (3/2)NkT

The expression for the entropy is,

S = int[dU/T] = klogW or klogU

From the above relations we conclude that options a, d, and e are having the greatest values of U and S.