The volume of gas is reduced to half from its original volume. The specific heat will be ___. (i) reduce to ha

NCERT Exemplar · Q4

Q. The volume of gas is reduced to half from its original volume. The specific heat will be ______.

(i) reduce to half

(ii) be doubled

(iii) remain constant

(iv) increase four times

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Concept understanding — Specific Heat Capacity

What is Specific Heat Capacity?

Imagine you have two identical stoves, two identical pots, and you put 1 kg of water in one pot and 1 kg of iron in the other. You turn both stoves to the same flame. After 2 minutes, the iron is scorching hot — you can't touch it. The water is still lukewarm.

Why? Because different substances need different amounts of heat to raise their temperature by the same amount. That's the core idea behind specific heat capacity.

The Intuition

Think of heat as "energy currency" and temperature rise as "buying a degree." Some materials are "cheap" — a little heat buys a big temperature rise. Others are "expensive" — you need to spend a lot of heat to get even a small rise.

Iron is cheap: a small heat input → large temperature jump.
Water is expensive: a large heat input → small temperature jump.

This "expensiveness" is what we call specific heat capacity. It tells you how much heat energy is needed to raise the temperature of 1 kg of a substance by 1 °C (or 1 K).

The Precise Definition

c = \frac{Q}{m \Delta T}

Where:

$c$ = specific heat capacity (J/kg·°C or J/kg·K)
$Q$ = heat energy supplied (J)
$m$ = mass of the substance (kg)
$\Delta T$ = change in temperature (°C or K)

In words: Specific heat capacity is the amount of heat required to raise the temperature of one kilogram of a substance by one degree Celsius (or one Kelvin).

Key Points to Remember

It's a property of the material, not the object. A small iron nail and a giant iron beam have the same $c$ value — but the beam needs more total heat because it has more mass.
Units matter. Common values:
- Water: $c = 4186 \text{ J/kg·°C}$ (or ≈ 4200 J/kg·°C in many problems)
- Iron: $c \approx 450 \text{ J/kg·°C}$
- Copper: $c \approx 390 \text{ J/kg·°C}$
Notice water's value is about 10 times that of iron — that's why water heats up so slowly compared to metals.
The formula works both ways. If a substance cools down, it releases the same amount of heat it would absorb to warm up by the same $\Delta T$ .

A Common Mistake to Avoid

Watch out

Don't confuse specific heat capacity ( $c$ ) with heat capacity ( $C$ ). Heat capacity is for an entire object: $C = mc$ . A large iron block can have a higher heat capacity than a small cup of water, even though iron's $c$ is much smaller. Always check: are we talking about per kg or for the whole thing?

Worked Example (Exam-Style)

Problem: How much heat is needed to raise the temperature of 2 kg of water from 20 °C to 50 °C? (Take $c_{\text{water}} = 4200 \text{ J/kg·°C}$ )

Solution:

$m = 2 \text{ kg}$
$\Delta T = 50 - 20 = 30 \text{ °C}$
$c = 4200 \text{ J/kg·°C}$

Q = mc\Delta T = 2 \times 4200 \times 30 = 252\,000 \text{ J} = 252 \text{ kJ}

Answer: 252 kJ of heat is required.

Why This Matters …

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Specific heat is an intrinsic property of a substance, meaning it depends on the nature of the material, not its quantity or volume. Therefore, reducing the volume of a gas does not change its specific heat. The specific heat will remain constant.

Concept and Intuition

Specific heat capacity, often denoted by $c$ (or $C$ for molar specific heat), is a fundamental thermodynamic property of a substance. It quantifies the amount of heat energy required to raise the temperature of a unit mass (or unit mole) of that substance by one degree Celsius (or Kelvin).

The crucial point here is that specific heat is an intensive property. This means its value depends solely on the nature of the substance itself – its chemical composition, molecular structure, and phase (solid, liquid, gas). It does not depend on the amount of the substance present, nor on its volume, shape, or any other extensive property.

For example, water always has a specific heat capacity of approximately $4186 \text{ J kg}^{-1} \text{ K}^{-1}$ at room temperature, whether you have a small cup or a large tank. Similarly, for a given gas, its specific heat capacity (whether at constant volume, $C_v$ , or constant pressure, $C_p$ ) is determined by the type of gas (e.g., monatomic like Helium, diatomic like Oxygen, or polyatomic like Carbon Dioxide) and its molecular structure, which dictates its degrees of freedom. Changing the volume of a fixed amount of gas does not alter the fundamental nature or molecular structure of the gas itself.

Step-by-step Solution

Understand Specific Heat: Specific heat capacity ( $c$ ) is defined as the heat energy ( $Q$ ) required to change the temperature ( $\Delta T$ ) of a unit mass ( $m$ ) of a substance:

c = \frac{Q}{m \Delta T}

For gases, we often consider specific heat at constant volume ($C_v$) or constant pressure ($C_p$), which are molar specific heats (per mole) or specific heats per unit mass.

2. Identify Property Type: Specific heat is an intensive property. This means it is characteristic of the material itself. It tells us how much energy is needed to heat that particular substance, regardless of how much of it we have or what its current volume is. …

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Q.The volume of gas is reduced to half from its original volume. The specific heat will be ______.

Concept and Intuition

Step-by-step Solution

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