Interactive Thermodynamics Laboratory
Latent Heat (Q = mL)
Latent heat is the "hidden" thermal energy that a substance absorbs or releases to change its state of matter (from solid to liquid, or liquid to gas) without changing its temperature. Witness this thermodynamic phase shift by running heating simulations, adjusting mass and power inputs, and watching the heating curve plateau in real-time.
Latent Heat Simulator
What is Latent Heat?
When you add heat energy to a block of ice, its temperature rises. However, the moment the ice reaches 0°C, the temperature stops rising, even though you continue heating it. The thermometer stays exactly at 0°C until every single ice crystal has melted into liquid water.
The thermal energy added during this period is called latent heat. Instead of raising the kinetic energy of the molecules (which determines temperature), this "hidden" heat is used entirely to break the rigid bonds holding the solid lattice together. Once the ice is fully melted, further heating will once again increase the temperature of the water until it hits 100°C, where it plateaus again to boil and turn into steam.
m = Mass of the substance undergoing phase change (kg)
L = Specific latent heat of the substance (J/kg)
For ice, Lf = 3.34 × 105 J/kg.
For water, Lv = 2.26 × 106 J/kg.
The Heating Curve of Water
A heating curve shows how temperature changes as heat energy is steadily added. The curve contains slanted lines and horizontal plateaus:
| Stage | State of Matter | Temperature Trend | Thermodynamic Process | Formula Used |
|---|---|---|---|---|
| 1 | Solid Ice (< 0°C) | Rising | Sensible heating of ice | Q = m × cice × ΔT |
| 2 | Ice & Water (0°C) | Flat (Plateau) | Melting (Latent heat of fusion) | Q = m × Lf |
| 3 | Liquid Water (0°C to 100°C) | Rising | Sensible heating of water | Q = m × cwater × ΔT |
| 4 | Water & Steam (100°C) | Flat (Plateau) | Boiling (Latent heat of vaporization) | Q = m × Lv |
| 5 | Steam (> 100°C) | Rising | Sensible heating of steam | Q = m × csteam × ΔT |
Real-Life Connections
Evaporative Cooling (Sweating)
When you sweat, the liquid water on your skin absorbs the latent heat of vaporization from your body to transition into gas. This transfers heat away from your skin, cooling your body down.
Refrigerators & Air Conditioners
Refrigeration cycles exploit latent heat. A liquid refrigerant is evaporated inside the cooling coils, absorbing latent heat from food compartments. The vapor is then compressed and condensed back to liquid outside, releasing the heat.
Protecting Crops from Frost
Farmers spray orange groves with water when temperatures dip below freezing. As the water freezes, it releases latent heat of fusion directly onto the fruit, keeping its temperature at 0°C and preventing freeze damage.
Solved Examples
Example 1 — Calculate the heat energy required to completely melt 0.50 kg of ice at 0°C. (Latent Heat of Fusion of ice, L_f = 3.34 × 10^5 J/kg)
• Identify the given values: mass (m) = 0.50 kg, latent heat of fusion (L_f) = 3.34 × 10^5 J/kg.
• Identify the phase change type: Solid (ice) to Liquid (water) at a constant temperature of 0°C. Use the formula: Q = m * L_f.
• Substitute the values into the formula: Q = 0.50 kg * (3.34 × 10^5 J/kg).
• Calculate the product: Q = 1.67 × 10^5 Joules = 167 kJ.
• Verify: The energy required is positive (absorbed) and equivalent to 167,000 Joules.
Final Answer: Q = 167 kJ (1.67 × 10^5 J)
Example 2 — A beaker contains 0.20 kg of boiling water at 100°C. An electric heater supplies 452,000 Joules of heat energy. How much water is converted into steam at 100°C? (Latent Heat of Vaporization, L_v = 2.26 × 10^6 J/kg)
• Identify the given values: heat supplied (Q) = 452,000 J, latent heat of vaporization (L_v) = 2.26 × 10^6 J/kg.
• Recall the phase change formula: Q = m * L_v, which rearranges to solve for mass converted: m = Q / L_v.
• Substitute the values: m = 452,000 J / (2.26 × 10^6 J/kg).
• Calculate the mass: m = 0.20 kg (or 200 g).
• Verify: Since 0.20 kg matches the initial water mass exactly, all of the water will be converted to steam.
Final Answer: m = 0.20 kg (200 g)
Example 3 — Find the total heat energy required to warm 0.10 kg of ice from -10°C to liquid water at 20°C. (Specific heat of ice = 2,220 J/kg·K, specific heat of water = 4,184 J/kg·K, latent heat of fusion = 3.34 × 10^5 J/kg)
• Break the process down into three steps:
• Step 1: Warm the ice from -10°C to 0°C. Q_1 = m * c_ice * ΔT = 0.10 kg * 2,220 J/kg·K * 10 K = 2,220 J.
• Step 2: Melt the ice at 0°C. Q_2 = m * L_f = 0.10 kg * (3.34 × 10^5 J/kg) = 33,400 J.
• Step 3: Warm the liquid water from 0°C to 20°C. Q_3 = m * c_water * ΔT = 0.10 kg * 4,184 J/kg·K * 20 K = 8,368 J.
• Sum the values to find the total heat energy: Q_total = Q_1 + Q_2 + Q_3 = 2,220 J + 33,400 J + 8,368 J = 43,988 Joules.
• Verify: The energy required is roughly 44 kJ, with melting (Step 2) taking up the vast majority (~76%) of the energy.
Final Answer: Q_total = 43,988 J (44.0 kJ)
Common Mistakes
❌ Applying Q = mcΔT during phase changes
Do not use specific heat formulas during melting or boiling! Because the temperature does not change, ΔT is 0. If you use Q = mcΔT, you would get Q = 0, which is incorrect. Use Q = mL instead.
❌ Mixing units (grams vs. kilograms)
Specific latent heat values are usually given in J/kg or kJ/kg. Make sure to convert the mass of your sample to kilograms before multiplying, or match mass units with L units.
❌ Forgetting multistep calculations
To heat ice at -10°C to water at 20°C, you cannot complete the calculation in a single formula step. You must calculate the heat for three separate stages (warming ice, melting ice, warming water) and sum them.
Quick Summary
- Latent heat is the heat energy absorbed or released during a phase change at constant temperature.
- Formula: Q = m × L. Melting uses Latent Heat of Fusion (L_f); boiling uses Latent Heat of Vaporization (L_v).
- Specific Latent Heat (L) is an intrinsic property with SI units of Joules per kilogram (J/kg).
- The heating curve features flat, horizontal sections where latent heating occurs, and slanted lines where sensible heating occurs.
- The latent heat of vaporization of water is much larger than its latent heat of fusion because vaporizing requires breaking all intermolecular bonds.
Practice Questions
- Question: Define "latent heat". Why does the temperature of a substance not change during a phase transition?
Reveal Answer & Explanation
Latent heat is the heat absorbed or released by a substance during a phase change that occurs at constant temperature. The temperature does not change because the thermal energy added is used to break or weaken intermolecular bonds rather than increasing the kinetic energy of the molecules.
- Question: How much heat energy is released when 0.35 kg of steam at 100°C condenses into liquid water at 100°C? (L_v = 2.26 × 10^6 J/kg)
Reveal Answer & Explanation
Using Q = m * L_v: Q = 0.35 kg * (2.26 × 10^6 J/kg) = 791,000 J = 791 kJ. Since it is condensation (gas to liquid), this energy is released to the surroundings.
- Question: A 1.5 kg metal block at 200°C is placed on a large block of ice at 0°C. If all the heat from the block goes into melting the ice, how much ice melts? (Specific heat of metal = 400 J/kg·K, L_f of ice = 3.34 × 10^5 J/kg)
Reveal Answer & Explanation
Heat lost by metal block: Q_lost = m * c * ΔT = 1.5 * 400 * (200 - 0) = 120,000 J. Heat gained by melting ice: Q_gained = m_ice * L_f. Set Q_lost = Q_gained: 120,000 J = m_ice * (3.34 × 10^5 J/kg) => m_ice = 120,000 / 334,000 ≈ 0.359 kg (359 g).
- Question: Explain why a steam burn at 100°C is generally much more severe than a hot water burn at 100°C.
Reveal Answer & Explanation
Steam contains a massive amount of latent heat of vaporization (2.26 × 10^6 J/kg). When steam hits the skin, it first condenses into liquid water at 100°C, releasing this large latent heat directly onto the skin. The remaining hot water at 100°C then cools down further, causing additional thermal damage.
- Question: Look at a typical heating curve graph. What do the flat, horizontal regions represent?
Reveal Answer & Explanation
The flat, horizontal regions represent phase transitions (melting or boiling) where latent heat is being absorbed or released. During these periods, the temperature of the substance remains constant.
- Question: Which is larger for water: the latent heat of fusion or the latent heat of vaporization? Explain why.
Reveal Answer & Explanation
The latent heat of vaporization (L_v = 2.26 × 10^6 J/kg) is much larger than the latent heat of fusion (L_f = 3.34 × 10^5 J/kg). Melting only requires weakening intermolecular bonds, whereas boiling requires breaking all bonds to completely separate the molecules into a gaseous state.
- Question: How much energy is needed to melt 10 grams of ice at 0°C? (L_f = 334 J/g)
Reveal Answer & Explanation
Using Q = m * L_f: m = 10 g, L_f = 334 J/g. Q = 10 * 334 = 3,340 J = 3.34 kJ.
Frequently Asked Questions
What is Latent Heat?
Latent heat is the thermal energy absorbed or released by a substance during a change in its physical state (phase change) that occurs without changing its temperature. The word "latent" comes from the Latin word for "hidden", referring to the heat added that does not show on a thermometer.
What is the formula for Latent Heat?
The formula is Q = m * L, where Q is the heat energy absorbed or released in Joules (J), m is the mass of the substance in kilograms (kg), and L is the specific latent heat of the substance in Joules per kilogram (J/kg).
What is Specific Latent Heat of Fusion?
The specific latent heat of fusion (L_f) is the heat energy required to change 1 kilogram of a substance from solid to liquid at its melting point without a change in temperature. For water/ice, L_f is approximately 3.34 × 10^5 J/kg.
What is Specific Latent Heat of Vaporization?
The specific latent heat of vaporization (L_v) is the heat energy required to change 1 kilogram of a substance from liquid to gas at its boiling point without a change in temperature. For water, L_v is approximately 2.26 × 10^6 J/kg.
Why does temperature stay constant during a phase change?
During a phase change, the added heat energy is used entirely to break or rearrange the intermolecular bonds holding the molecules together, rather than increasing their average kinetic energy. Since temperature is a measure of average molecular kinetic energy, the temperature remains constant.
What is the difference between latent heat and sensible heat?
Sensible heat is heat energy that causes a change in the temperature of a substance (which can be "sensed" by a thermometer). Latent heat is heat energy that causes a phase change at a constant temperature (the thermometer reading remains flat).
What is the heating curve of a substance?
A heating curve is a graph plotting temperature against heat energy added (or time under constant heating). It features slanted lines representing regions where the substance warms up (sensible heating) and flat horizontal plateaus representing phase transitions (latent heating).
Why is water's latent heat of vaporization so high?
Water has a very high latent heat of vaporization because of the strong hydrogen bonds holding the liquid water molecules together. A massive amount of energy is required to break these bonds and transition water into steam.
What happens to latent heat during freezing?
During freezing (liquid to solid), the substance releases latent heat to its surroundings as molecules settle into a rigid lattice structure. The temperature remains at the freezing point until all liquid has solidified.
How does sweat cool our bodies?
Sweat is liquid water on the skin. As it evaporates, it absorbs latent heat of vaporization from our body to transition into water vapor. This removes excess thermal energy and lowers our skin temperature.
What is sublimation and does it involve latent heat?
Sublimation is the direct transition of a substance from solid to gas (e.g. dry ice). It requires latent heat of sublimation, which is the sum of the latent heats of fusion and vaporization.
What is the SI unit of Specific Latent Heat?
The SI unit of specific latent heat is Joules per kilogram (J/kg). Other common units include Joules per gram (J/g) and calories per gram (cal/g).