Thermal capacity of a body depends on the
- (a)mass of the body only
- (b)mass and shape of the body only
- (c)density of the body
- (d)mass, shape and temperature of the body
Correct — A, mass of the body only. Thermal capacity is the heat needed to raise the whole body through one degree, and it is given by the product of the mass and the specific heat of the material: C = m × c. Of the four candidate quantities the paper offers, only mass appears in that product. Shape does not enter it, which rules out options (b) and (d); temperature does not enter it either, which finishes off (d); and density is not a factor, which disposes of (c), since a body's thermal capacity is fixed by how much matter it contains and not by how tightly that matter is packed. For a given material, then, thermal capacity is proportional to mass and to nothing else on this list.
- (b)mass and shape of the body only — Shape has no place in C = m × c. What shape does change is the surface area, and therefore how quickly heat enters or leaves the body — a rate, not a capacity. Roll a kilogram of copper into a sphere or beat it into a sheet and it still needs the same energy to warm by one degree.
- (c)density of the body — Density tells you mass per unit volume, not mass. A dense small object and a light bulky one can have identical thermal capacity if their masses and materials match. Density enters only indirectly, through the mass of a body of stated volume.
- (d)mass, shape and temperature of the body — This piles on two extra dependencies that the formula does not have. Specific heat does drift slightly with temperature in real substances, but at the level being tested here neither shape nor temperature is a variable in the thermal capacity of a body.
Thermal capacity — also called heat capacity — is measured in joules per kelvin and describes the whole body. Divide it by mass and you obtain specific heat capacity in joules per kilogram per kelvin, which describes the material. The pair is exactly analogous to weight and density: one belongs to the object, the other to the substance. A closely related idea is the water equivalent, the mass of water that would have the same thermal capacity as the body, which is why calorimetry problems can add a calorimeter's contribution simply as extra grams of water.
One tension in this item should be stated plainly rather than papered over. Strictly, thermal capacity depends on two things — the mass and the specific heat of the material — so the word 'only' in option (a) is not the whole truth about the physics. It is nevertheless the right answer to the question asked, because the examiner is testing which of four listed quantities the capacity varies with, and the material is not among the four. Answer the option set you are given: of mass, shape, density and temperature, only mass belongs. This item and question 101 of the same paper form a matched pair. There, specific heat is declared independent of mass and shape; here, thermal capacity is declared dependent on mass. A candidate who reads them together sees the point of both — dividing by mass is what turns a property of the object into a property of the substance.
- Thermal capacity C = m × c, and its SI unit is the joule per kelvin.
- Specific heat capacity is thermal capacity per unit mass, in joules per kilogram per kelvin.
- Shape affects the rate at which heat enters or leaves a body, not the energy it stores per degree.
- The water equivalent of a body is the mass of water having the same thermal capacity as that body.
Write the formula first and the option set answers itself.
- Adding shape to any thermal quantity because shape matters for cooling rates.
- Substituting density for mass when the two are not the same thing.
- Missing that this item and question 101 of the same paper are two halves of one definition.
NDA sets one heat-definition item per paper, and the distractors are almost always shape, density and temperature added to a formula that contains none of them.
Assertion (A): To dilute sulphuric acid, acid is added to water and not water to acid. Reason (R): Specific heat of water is quite large.
- (a) Both A and R are true, and R is the correct explanation of A
- (b) Both A and R are true, but R is not a correct explanation of A
- (c) A is true, but R is false
- (d) A is false, but R is true
Answer(a) Both A and R are true, and R is the correct explanation of A
A laboratory consequence of the same product — a large mass of water with a high specific heat gives a large thermal capacity, which is what safely soaks up the heat of dilution.
What is the mass of a material, whose specific heat capacity is 400 J/(kg °C) for a rise in temperature from 15 °C to 25 °C, when heat received is 20 kJ?
- (a) 0·1 kg
- (b) 1 kg
- (c) 10 kg
- (d) 5 kg
Answer(d) 5 kg
The same relation used as an equation rather than a definition, and the reason mass is the only variable of the four this item offers.
The amount of heat required to change a liquid to gaseous state without any change in temperature is known as
- (a) specific heat capacity
- (b) mechanical equivalent of heat
- (c) latent heat of vaporization
- (d) quenching
Answer(c) latent heat of vaporization
The third quantity in this family, offered with specific heat as its leading distractor — worth learning beside thermal capacity so that all three definitions stay separate.
- practice — not a real PYQ
The SI unit of thermal capacity is
- (a)J kg⁻¹ K⁻¹
- (b)J K⁻¹
- (c)J kg⁻¹
- (d)W m⁻¹ K⁻¹
Answer(b) J K⁻¹ — joules per kelvin, since thermal capacity is defined for the whole body rather than per kilogram.
- practice — not a real PYQ
The water equivalent of a body is
- (a)the volume of water it displaces
- (b)the mass of water having the same thermal capacity as the body
- (c)the mass of water the body can absorb
- (d)the temperature at which the body melts in water
Answer(b) the mass of water having the same thermal capacity as the body — a device that simplifies calorimetry.