--- title: "Specific heat capacity and specific latent heat in calculations" description: "Calculate warming stages with Q = mcΔT and melting or boiling stages with Q = mL. For a pure substance at constant pressure, temperature stays constant during melting or boiling. Add stage energies an" canonical: https://lightmysky.com/learn/science/specific-heat-capacity-and-specific-latent-heat-in-calculations-mt_GKNPAJgroW source: https://lightmysky.com/learn/science/specific-heat-capacity-and-specific-latent-heat-in-calculations-mt_GKNPAJgroW.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Specific heat capacity and specific latent heat in calculations Calculate warming stages with Q = mcΔT and melting or boiling stages with Q = mL. For a pure substance at constant pressure, temperature stays constant during melting or boiling. Add stage energies and distinguish heater output from energy reaching the sample. Subject: Science · Area: Energy · Ages 15 to 17 Page: https://lightmysky.com/learn/science/specific-heat-capacity-and-specific-latent-heat-in-calculations-mt_GKNPAJgroW ## Ready when they can - Works a multi-stage problem that both warms and melts a sample - Reads a temperature-time graph and names the flat sections as changes of state - Uses a heater's power and running time as the energy supplied, and comments on losses to the surroundings ## Lesson: Warming, melting and heater maths You have used Q = mcΔT for warming without a state change. Q is energy absorbed in J, m is mass in kg, c is in J/(kg°C), and ΔT is final minus initial temperature in °C. Divide grams by 1000 to get kg. Use c for the current state: about 2100 for ice and 4200 for liquid water. Warming ice from -10°C to 0°C gives a rise of 10°C. For melting or boiling, use Q = mL. Specific latent heat, L, is energy per kilogram for that state change, in J/kg. Choose the melting or boiling value as needed. Pure water melts at about 0°C and boils at about 100°C at normal atmospheric pressure. During either change at constant pressure, temperature stays constant. Energy changes particle arrangements and interactions, not the chemical bonds within water molecules. *(drawing: Use the equation for each stage, then add the stage energies.)* **Example.** Take 0.1 kg of ice at -5°C to water at 20°C at normal atmospheric pressure. Use c_ice = 2100 J/(kg°C), L = 334000 J/kg and c_water = 4200 J/(kg°C). Warm ice: 0.1 x 2100 x 5 = 1050 J. Melt: 0.1 x 334000 = 33400 J. Warm water: 0.1 x 4200 x 20 = 8400 J. Add them: 1050 + 33400 + 8400 = 42850 J absorbed. Ignore transfers elsewhere. Heater output is E = Pt: power in W times time in s gives energy in J. One watt is one joule per second. A 60 W heater running for 90 s supplies 5400 J. If 1000 J warms the container and surroundings, the sample receives 4400 J. Subtract stated transfers elsewhere before using sample energy in mcΔT or mL. To reach the same final state with losses, the heater must supply more energy. *(drawing: Energy account in J: 5400 supplied = 4400 to the sample + 1000 elsewhere.)* A heating curve plots temperature vertically against time horizontally. With positive net energy entering a pure sample at constant pressure, rising sections show warming and horizontal sections show melting or boiling. For water at normal atmospheric pressure, the 0°C plateau shows melting and the 100°C plateau shows boiling. A flat trace alone does not prove a state change: temperature can also stay steady when no net energy enters. If only part of the ice melts, subtract any earlier warming energy first. The energy left for melting gives melted mass = Q/L. For example, 3340 J available for melting with L = 334000 J/kg melts 0.01 kg. Compare this with the starting mass to check whether ice remains. During melting at constant pressure, ΔT = 0 does not mean no energy is needed: mL is positive for a positive melted mass. **Recap.** Use mcΔT for warming and mL for melting or boiling. Add stage energies. Heater output is Pt; subtract transfers elsewhere to find energy reaching the sample. *Lesson, questions and flashcards written for this dataset. OpenStax textbook records were consulted for scientific facts and problem structures; their prose was not reproduced.* ## Practice 14 questions on this page, each with its working shown. ## Needs first - [Specific heat capacity as a material property](https://lightmysky.com/learn/science/specific-heat-capacity-as-a-material-property-mt_mXC9IKom3P) ## Optional connections - [Internal Energy, Absolute Zero and the Kelvin Scale](https://lightmysky.com/learn/science/internal-energy-absolute-zero-and-the-kelvin-scale-mt_n4Ku8ZDy1U)