Which substance in table 5.2 requires the smallest amount of energy to increase the temperature of 51.5g of that substance by 10k ?
all of these are specific heats of some substances at 298 k.
so n2(g) is 1.04 j/g-k
al (s) .90 j/g-k
fe (s) .45 j/g-k
hg (l) .14j/g-k
h2o (l) 4.18 j/g-k
ch4 (g) 2.20 j/g-k
co2 (g) .84 j/g-k
caco3 (s) .82 j/g-k

Because we are considering the same amount of each substance and the temperature change is also the same, we can directly compare the specific heat capacities of the substances. The lower the heat capacity, the easier it is to raise the temperature of the substance.
As seen from the table, Mercury (Hg) has the lowest heat capacity; requiring only 0.14 Joules per g per kelvin. The energy needed for the given amount and temperature change:
0.14 x 51.5 x 10
= 72.1 Joules

Sorry i dont understand the question can you rephase it?