The densities of two substances are in the ratio 5:6 and the specific heats are in the ratio 3:5 respectively. The ratio of their thermal capacities per unit volume is

C= c•ρ

C1/C2 = c1• ρ1/ c2• ρ2 =3•5/5•6 =1/2.

Full mathod

To find the ratio of thermal capacities per unit volume, we need to consider the density and specific heat of the two substances.

Let's denote the densities of the two substances as D1 and D2, and their specific heats as C1 and C2, respectively.

Given that the densities are in the ratio 5:6, we can say that D1/D2 = 5/6.
Similarly, the specific heats are in the ratio 3:5, so C1/C2 = 3/5.

Now, let's find the thermal capacities per unit volume. The thermal capacity per unit volume is given by the product of density and specific heat, i.e., thermal capacity per unit volume = density * specific heat.

For the first substance, the thermal capacity per unit volume (Cv1) is given by Cv1 = D1 * C1.
Similarly, for the second substance, the thermal capacity per unit volume (Cv2) is given by Cv2 = D2 * C2.

Now, let's substitute the ratios we have and find the ratio of their thermal capacities per unit volume:

Cv1/Cv2 = (D1 * C1) / (D2 * C2)

Substituting the given ratios:

Cv1/Cv2 = ((5/6) * (3/5)) / (1 * 1)

Simplifying, we get:

Cv1/Cv2 = (15/30) / 1

Cv1/Cv2 = 1/2

Therefore, the ratio of their thermal capacities per unit volume is 1:2.