The ratio of thermal capacities of two spheres A and B, if...

The ratio of thermal capacities of two spheres $A$ and $B$, if their diameters are in the ratio $1: 2$, densities in the ratio $2: 1$, and the specific heat in the ratio of $1: 3$, will be:
(a) $1: 6$
(b) $1: 12$
(c) $1: 3$
(d) $1: 4$

Key Concepts

Thermal Capacity

Thermal capacity refers to the ability of an object to store heat energy. It is determined by both the mass of the material and its specific heat capacity, representing the total amount of heat required to raise the temperature of the object by a given amount.

Mass-Density Relationship

The mass of an object is obtained by multiplying its density by its volume. This relationship is crucial in determining how much material is present to store thermal energy, particularly when comparing objects of differing densities.

Volume Scaling in Geometry

For geometrically similar objects like spheres, volume scales with the cube of their linear dimensions (such as the diameter). This geometric scaling principle is essential when comparing the masses and thermal capacities of objects of different sizes.

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates how much energy is needed to raise the temperature of a unit mass by one degree. It plays a key role in determining thermal capacity when combined with mass.

Proportional Reasoning in Physics

Proportional reasoning involves using ratios to compare physical quantities. In problems involving scaling dimensions, densities, and specific heat capacities, setting up and simplifying ratios allows one to understand how changes in these quantities influence overall properties like thermal capacity.

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