Heat

Heat is the flow of energy that occurs because of a temperature difference — and it always flows one direction, from the hotter object to the colder one. This article covers how heat differs from temperature, how heat capacity connects the two through the formula q = mcΔT, the specific heat of water as a reference value, and calorimetry — specifically constant-volume (bomb) calorimetry, where a simplifying condition makes heat easy to measure directly.

Key Takeaways

• Heat is energy transfer driven by a temperature difference, always flowing from the hotter object to the colder one; temperature measures a system's average particle kinetic energy — related concepts, but not the same thing.

• Heat capacity is the heat needed to raise a substance's temperature by 1°C; specific heat capacity is that value per gram, molar heat capacity is that value per mole.

• q = mcΔT calculates heat from mass, specific heat, and temperature change; the specific heat of water is 4.18 J/(g·K).

• Calorimetry measures heat changes using a calorimeter; the two common types are constant-volume and constant-pressure calorimeters.

• In a bomb calorimeter (constant volume), ΔV = 0 means no P-V work is done (w = 0), so ΔE = q_v — all the internal energy change is captured directly as measured heat, making bomb calorimeters well-suited to combustion reactions.

Heat vs. Temperature

Heat and temperature are related but not the same thing. Temperature measures the average kinetic energy of a system's particles — how fast those particles are moving, on average. Heat measures the transfer of that kinetic energy from one system to another. A system has a temperature at any given moment; heat only exists as energy moving between systems when a temperature difference drives that transfer.

Heat Capacity, Specific Heat, and Molar Heat Capacity

Although heat and temperature aren't the same property, a temperature change can be used to calculate heat — the link between them is heat capacity.

• Heat capacity: the amount of heat required to raise a substance's temperature by 1°C.

• Specific heat capacity: the heat capacity of 1 gram of a substance.

• Molar heat capacity: the amount of heat required to raise the temperature of 1 mole of a substance by 1°C.

The q = mcΔT Formula

If the specific heat capacity of a substance is known, heat can be calculated with:

q = m × c × ΔT

where q is heat, m is mass, c is specific heat, and ΔT is the temperature change. c can be expressed in units of per °C or per K, and ΔT works out to the same numeric value in either scale, since both are equal-sized temperature-difference units.

One especially useful reference value: the specific heat of water is 4.18 J/(g·K) (equivalently, J/(g·°C)).

Worked example — heat required to raise 250 g of water from 20°C to 80°C:

• ΔT = 80°C − 20°C = 60°C (= 60 K, since it's a temperature difference)

• q = m × c × ΔT = 250 g × 4.18 J/(g·K) × 60 K

• q = 62,700 J (62.7 kJ)

Calorimetry

Calorimetry is the technique used to measure the heat involved in a chemical or physical change. The instrument used to make that measurement is called a calorimeter. There are two common types: constant-volume calorimeters and constant-pressure calorimeters.

At its core, calorimetry rests on a simple principle: when a substance undergoes a chemical reaction or physical change inside a calorimeter, heat is either absorbed or released, and measuring that heat change reveals thermodynamic properties of the substance — like the ones covered below for the constant-volume case.

Constant-Volume (Bomb) Calorimetry

Constant-volume calorimetry is typically carried out in a bomb calorimeter — a rigid, sealed container built to withstand high internal pressure without rupturing (hence "bomb").

Because the container's volume doesn't change, ΔV = 0. Recall that pressure-volume work is defined as w = −PΔV — with ΔV = 0, no work is done at all (w = 0). Since the change in internal energy is ΔE = q + w, and w = 0 here, the heat measured at constant volume (q_v) accounts for the entire change in internal energy:

ΔE = q_v

That's what makes bomb calorimeters especially useful for studying combustion reactions: since no pressure-volume work complicates the picture, the considerable heat these reactions release can be measured directly and accurately as q_v, with no additional correction needed.

Common MCAT Mistakes

• Treating heat and temperature as the same quantity. Temperature is a property a system has at a given moment; heat is energy in transit, existing only when a temperature difference drives a transfer between systems.

• Confusing specific heat capacity with molar heat capacity. Specific heat capacity is heat per gram per °C; molar heat capacity is heat per mole per °C — using the wrong one (or the wrong mass/mole quantity) in q = mcΔT gives an answer off by the substance's molar mass.

• Forgetting that a temperature difference (ΔT) has the same numeric value in Celsius and Kelvin. Absolute temperatures require converting to Kelvin, but since both scales have equal-sized degree increments, a ΔT of 60°C is also a ΔT of 60 K — no conversion needed for the ΔT term itself in q = mcΔT.

• Assuming pressure-volume work must be accounted for in every calorimetry problem. In a bomb (constant-volume) calorimeter, ΔV = 0 by construction, so w = 0 and ΔE = q_v directly — no separate work correction is needed, which is precisely what makes bomb calorimetry convenient for measuring combustion heat.

MCAT-Style Concept Check

Question: A 500 g sample of water is heated from 25°C to 45°C. Using the specific heat of water (4.18 J/(g·K)), how much heat was absorbed by the water?

• A) 20.9 kJ

• B) 41.8 kJ

• C) 83.6 kJ

• D) 209 kJ

Answer: B

Explanation: ΔT = 45°C − 25°C = 20°C = 20 K. Applying q = mcΔT: q = 500 g × 4.18 J/(g·K) × 20 K = 41,800 J = 41.8 kJ.

FAQ

What's the difference between heat capacity and specific heat capacity?

Heat capacity is the heat needed to raise an entire sample's temperature by 1°C, and it depends on how much substance is present. Specific heat capacity is heat capacity normalized to 1 gram, making it an intrinsic property of the substance itself rather than of a particular sample size.

What is q = mcΔT used for?

It calculates the heat (q) absorbed or released when a substance's temperature changes, using its mass (m), specific heat capacity (c), and the temperature change (ΔT). It only applies within a single phase — it doesn't cover the heat absorbed or released during a phase change itself.

Why does ΔV = 0 in a bomb calorimeter matter for calculating ΔE?

Because pressure-volume work is w = −PΔV, a fixed volume (ΔV = 0) means no work is done (w = 0). Since ΔE = q + w, that leaves ΔE = q_v — the heat measured at constant volume directly equals the full change in internal energy, with no separate work term to account for.

What is the specific heat of water?

4.18 J/(g·K), equivalently written 4.18 J/(g·°C) since a temperature difference has the same numeric value in both scales. It's a commonly tested reference value because water is the solvent in most calorimetry and biological contexts on the MCAT.