One mole of ice at $273 K$ is melted ( $Δ_{f u s} H = 6010 J mo l^{- 1}$ ) and the water is then heated reversibly to $353 K$ ( $C_{P, m} = 75.3 J mo l^{- 1} K^{- 1}$ , constant). Which statements are correct?

AThe entropy change on melting is about $22.0 J K^{- 1}$ .
BThe entropy change on heating the liquid is about $19.4 J K^{- 1}$ .
CThe total entropy change of the water is about $41.4 J K^{- 1}$ .
DIf the heating is done by a single hot plate at $353 K$ , $Δ S_{u ni v erse}$ for the heating step is zero.

Answer: A, B, C

Melting:

6010/273 = 22.01

. Heating:

75.3 ln (353/273) = 19.35

. Total

= 41.37 J K^{- 1}

(A, B, C true). Using

C_{P} Δ T / T_{f}

would give

17.1

, which is wrong. With one hot plate at

353 K

the heat transfer is irreversible: the plate loses only

75.3 (80) /353 = 17.1

of entropy, less than the water gains (19.4), so

Δ S_{u ni v} > 0

(D false).