Thermal Energy Study Guide
Calculating Heat
Heat (Q): The energy transferred between substances due to a temperature difference. It can raise the temperature of a substance or cause a phase change.
Mass (m): The amount of substance being heated or cooled, measured in grams (g) or kilograms (kg).
Specific Heat (c): The amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius (°C). It varies for different materials.
Change in Temperature (ΔT): The difference between the final temperature (Tf) and the initial temperature (Ti) of the substance:
ΔT = Tf - Ti
Formula for Calculating Heat
Q = m ⋅ c ⋅ ΔT
Q = heat transferred (joules, J)
m = mass (grams or kilograms)
c = specific heat (J/g°C; J/kg°C; J/gK; J/kgK)
ΔT = change in temperature (°C or K)
Example:
Calculate the heat required to heat 200 grams of water from 25.0 °C to 100.0°C. (Assume the specific heat of liquid water is 4.18 J/g°C).
Step 1: Identify Given Values
Mass (m): 200 g
Specific Heat (c): 4.18 J/g°C
Initial Temperature (Ti): 25.0 °C
Final Temperature (Tf): 100.0 °C
Step 2: Calculate Change in Temperature
ΔT = Tf - Ti → ΔT = 100 - 25 = 75oC
ΔT = 75oC
Step 3: Substitute Values into the Formula
Q = m ⋅ c ⋅ ΔT
Q = 200 x 4.18 x 75
Step 4: Perform the Calculation - multiply and convert the units to joules.
Q = 200 ⋅ 4.18 ⋅ 75.0 → Q = 62700 J
I. Core Concepts
A. Thermal Energy (TE)
1. Definition: total kinetic energy of all
moving particles in a substance
2. Key points
a. All matter has thermal energy
(even objects that feel cold)
b. TE depends on temperature
(average energy per particle) and
mass (number of particles - can be extended to volume)
3. Example: tub of warm water vs.
small pot of boiling soup
a. Soup: higher temperature (higher
average kinetic energy)
b. Tub: greater mass (more particles)
→ can have greater TE overall
B. Temperature
1. Definition: average kinetic energy of
particles in matter
2. Key points
a. Higher temperature → particles
move faster on average
b. Temperature determines how
warm/cool something feels
3. Example: person with fever —
thermometer measures raised average
particle energy.
C. Relationship: Thermal Energy vs.
Temperature vs. Mass
1. Temperature = average kinetic energy
per particle
2. Thermal energy = sum of kinetic
energies.
a. TE = (average energy) × (number
of particles related to mass)
3. Thought experiments
a. Large ice block could have more TE
than small pot of boiling water
if mass is much larger
b. Small hot object vs. large warm
object comparisons
II. Measurement of Temperature
A. Thermometers (liquid-in-glass)
1. Working principle: liquid expands when
warmer, contracts when cooler
2. Explanation: particle motion increases
spacing → liquid rises; decreases
→ liquid falls
B. Temperature Scales
1. Kelvin (SI)
a. Freezing point of water: 273 K
b. Boiling point of water: 373 K
c. Temperatures not given in
“degrees”
2. Celsius
a. Freezing point: 0 °C
b. Boiling point: 100 °C
3. Fahrenheit
a. Freezing point: 32 °F
b. Boiling point: 212 °F
4. Conversions
a. Celsius 
Kelvin
i. K = °C + 273
ii. °C = K − 273
b. Celsius → Fahrenheit
i. °F = (°C × 1.8) + 32
c. Fahrenheit → Celsius
i. °C = (°F − 32) ÷ 1.8
5. Examples
a. 10 °C = 283 K and = 50 °F
b. 86 °F → (86 − 32) ÷ 1.8 = 30 °C
III. Heat (Energy Transfer)
A. Heat = transfer of thermal energy between
substances
B. Direction and mechanism
1. Thermal energy always moves from
warmer to cooler substances
2. Collisions: faster-moving particles
(those with higher kinetic energy)
transfer energy to slower-moving
particles (those with lower kinetic
energy) until equilibrium
C. Examples
1. Oven heating food: oven → food
2. Ice in cola: cola transfers thermal
energy to ice → ice melts; cola cools
IV. Specific Heat Capacity
A. Definition
1. Amount of energy required to raise one
mass unit of a substance by one
temperature unit
2. Units: J/kgK; J/g·K; J/gC; J/kgC
B. Importance
1. Property specific to each material
2. Explains different heating/cooling rates
of substances
C. Sample specific heat values (J/kgK)
1. Iron ≈ 450
2. Sand ≈ 670
3. Wood ≈ 1760
4. Water ≈ 4180
D. Applications & examples
1. Beach: sand heats quickly (low specific
heat) vs. water remains cooler
(high specific heat)
2. Cooking: metal pots heat quickly;
wooden handles safer due to higher
specific heat and lower conductivity
3. Hot tea vs. hot soup: soup often cools
more slowly because of higher
specific heat and/or greater mass
V. Vocabulary Summary
A. Thermal Energy: total kinetic energy of
particles
B. Temperature: average kinetic energy of
particles
C. Kinetic Energy: energy due to motion
D. Mass: amount of matter; affects total TE
E. Thermometer: device to measure
temperature (liquid expansion)
F. Specific Heat: energy per mass per degree
to raise temperature
G. Kelvin / Celsius / Fahrenheit: temperature
scales
