Which of the following statements about specific heat of a body is/are correct ? 1. It depends upon mass and shape of the body 2. It is independent of mass and shape of the body 3. It depends only upon the temperature of the body Select the correct answer using the code given below :
- (a)1 only
- (b)2 and 3
- (c)1 and 3
- (d)2 only
Correct — D, 2 only. Specific heat is defined per unit mass — it is the heat needed to raise one kilogram of a substance through one degree — so the mass has already been divided out before the number is quoted. What is left over is a property of the material and nothing else: about 4,180 joules per kilogram per kelvin for water, about 900 for aluminium, about 385 for copper. The same figure holds for a gram of copper and for a tonne of it, for a copper sphere and for a copper sheet. Statement 2 says precisely this and is the only correct one of the three. Statement 1 asserts the opposite. Statement 3 collapses on the word 'only' — the value does drift slightly as a substance is heated, but what fixes it in the first place is which substance it is, not what the thermometer reads.
- (a)1 only — Statement 1 is the exact opposite of the truth, and it is the description of a different quantity — thermal capacity, which equals mass multiplied by specific heat and therefore does grow with mass. Shape does not enter either quantity; it changes how fast heat gets in through the surface, not how much energy the body stores per degree.
- (b)2 and 3 — Statement 2 is right, so this is the near-miss the paper is built around, but statement 3 is not. Saying specific heat depends 'only upon the temperature' throws away the one thing that actually decides it — the material. Water and copper at the same temperature have specific heats that differ by more than tenfold.
- (c)1 and 3 — Both of these statements are false, and picking them means treating specific heat as though it belonged to the particular lump of matter in front of you rather than to the substance it is made of.
Heat capacity and specific heat are two rungs of the same idea. The thermal (or heat) capacity of a body is the energy needed to raise that whole body by one degree, measured in joules per kelvin, and it naturally scales with how much matter is present. Divide it by the mass and you get specific heat capacity, in joules per kilogram per kelvin, which is a constant of the material. The definition is what settles this item: because 'per kilogram' is built into it, doubling the sample cannot change the number.
Read a statement-code item like this one for the quantifiers before anything else. Statement 3 would be defensible if it said 'varies somewhat with temperature' — real specific heats do rise or fall by a few per cent over a wide temperature range, and near absolute zero they fall away sharply. The word 'only' is what makes it false, because it silently drops the material from a property that is defined by the material. The same paper sets the mirror image of this item at question 120, which asks what thermal capacity depends on and expects the answer 'mass', so a candidate who has the two definitions straight collects both marks; one who blurs them is likely to lose both. Shape is a red herring planted in statement 1: a flat sheet cools faster than a sphere of the same metal and mass, but that is a statement about the rate of transfer across a surface, not about how much energy each kilogram must absorb to warm by a degree.
- Specific heat capacity is heat per unit mass per unit temperature rise; its SI unit is the joule per kilogram per kelvin.
- Water's specific heat is about 4,180 J per kg per kelvin — unusually high, which is why water works so well as a coolant and why the sea warms and cools more slowly than the land beside it.
- Thermal capacity equals mass multiplied by specific heat and is measured in joules per kelvin; that quantity does depend on mass.
- Latent heat is a third quantity again — the heat absorbed at a change of state with no temperature change at all.
Statement 1 describes the middle row, not the top one — which is the entire trap in this item.
- Treating specific heat and thermal capacity as the same quantity — one is per kilogram, the other is for the whole body.
- Assuming that anything with the word 'heat' in its name must scale with the amount of matter.
- Skimming past 'only' in a statement that is otherwise half true.
NDA sets at least one item a paper on the boundary between a per-unit-mass property and a whole-body quantity, either as a statement code like this or as a one-line numerical.
Consider the following statements : Statement-I : The temperature contrast between continents and oceans is greater during summer than in winter. Statement-II : The specific heat of water is more than that of land surface. Which one of the following is correct in respect of the above statements?
- (a) Both Statement-I and Statement-II are correct and Statement-II is the correct explanation for Statement-I
- (b) Both Statement-I and Statement-II are correct and Statement-II is not the correct explanation for Statement-I
- (c) Statement-I is correct but Statement-II is incorrect
- (d) Statement-I is incorrect but Statement-II is correct
Answer(d) Statement-I is incorrect but Statement-II is correct
UPSC uses the same property in a geography setting — water's specific heat is higher than land's, which is a statement about the two materials and not about how much of each there is.
Which one of the following statements is NOT correct ?
- (a) In the conduction mode of transference of heat, the molecules of solid pass heat from one molecule to another without moving from their positions
- (b) The amount of heat required to raise the temperature of a substance is called its specific heat capacity
- (c) The process of heat transfer in liquids and gases is through convection mode
- (d) The process of heat transfer from a body at higher temperature to a body at lower temperature without heating the space between them is known as radiation
Answer(b) The amount of heat required to raise the temperature of a substance is called its specific heat capacity
The same definition tested a year earlier, and marked wrong for leaving out 'per unit mass' and 'per degree' — exactly the words that make statement 2 of this item true.
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 numerical form of the same relation; the mass is what you solve for precisely because the specific heat is a fixed property of the material.
- practice — not a real PYQ
Two blocks of the same metal, one of mass 1 kg and one of mass 5 kg, are at the same temperature. Which quantity is the same for both?
- (a)Thermal capacity
- (b)Specific heat capacity
- (c)Total heat needed to raise the temperature by 10 degrees
- (d)Water equivalent
Answer(b) Specific heat capacity — it is a property of the metal, while the other three all scale with mass.
- practice — not a real PYQ
The SI unit of specific heat capacity is
- (a)J K⁻¹
- (b)J kg⁻¹
- (c)J kg⁻¹ K⁻¹
- (d)J kg K
Answer(c) J kg⁻¹ K⁻¹ — joules per kilogram per kelvin; J K⁻¹ alone is the unit of thermal capacity.