Example 1 — Find heat \(q\)
Aluminum sample: \(m = 120\,\text{g}\), \(c = 0.900\,\mathrm{J\,g^{-1}\,^\circ C^{-1}}\), \(\Delta T = 15.0\,^\circ\text{C}\).
Specific Heat Calculator
Specific Heat Calculator computes c, q, m, ΔT with clear equations, unit-aware guidance, and stepwise examples for labs and reports.
Choose the unknown you want the calculator to compute.
Either enter ΔT directly, or enter Ti and Tf to compute ΔT.
Equation Preview
c = Q / (m·ΔT)
Helping Notes
- Use consistent units; this tool converts automatically to compute correctly.
- Sign convention: positive Q or ΔT indicates heating; negative indicates cooling.
- ΔT in °C equals ΔT in K. For °F differences, ΔT(°C) = ΔT(°F) × 5/9.
Results
Primary Result
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Computed ΔT & Consistency
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Worked Steps
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What Is a Specific Heat Calculator?
A Specific Heat Calculator is a tool for experiments and learning that relates heat energy \(q\), mass \(m\), temperature change \(\Delta T\), and specific heat capacity \(c\). In thermochemistry, the core relationship
quantifies energy absorbed or released when a substance changes temperature without a phase change. The calculator solves for any one variable given the other three, checks unit consistency, and emphasizes correct sign conventions and significant figures. It is ideal for classroom exercises, lab planning, and homework verification.About the Specific Heat Calculator
The calculator applies the constant-pressure calorimetry model. Input values for heat energy \(q\), mass \(m\), temperature change \(\Delta T\), and specific heat capacity \(c\). The missing variable is computed using
.Supported units include: \(q\) in J or kJ, \(m\) in g or kg, and \(\Delta T\) in °C or K (numerically identical for differences). Specific heat \(c\) can be in \(\mathrm{J\,g^{-1}\,^\circ C^{-1}}\) or \(\mathrm{J\,kg^{-1}\,K^{-1}}\).
For thermal equilibrium problems, the energy balance equation
computes unknown temperatures or specific heats. Optionally, a calorimeter constant \(C_{\text{cal}}\) accounts for heat absorbed by the container:How to Use This Specific Heat Calculator
- Select the variable to solve for: \(q\), \(m\), \(c\), or \(\Delta T\).
- Enter known values using consistent units. For temperature change, use \(\Delta T = T_{\text{final}} - T_{\text{initial}}\).
- Click calculate to see the solved value, unit-checked equation, and interpretation.
- For mixing problems, input both masses and initial temperatures; the tool applies energy balance to find the unknown.
- Record results with appropriate significant figures and units for reports.
Core Formulas (LaTeX)
Sensible heating/cooling:
Solve for specific heat:
Solve for mass or temperature change:
Mixture at equilibrium (no losses):
With calorimeter constant \(C_{\text{cal}}\) (optional):
Examples
Example 2 — Find specific heat \(c\)
Metal sample: \(m = 250\,\text{g}\), \(q = 3.15\,\text{kJ}\), \(\Delta T = 10.0\,^\circ\text{C}\).
Example 3 — Coffee-cup calorimetry
Mix hot water: \(m_h = 100.0\,\text{g}, T_{h,i} = 60.0\,^\circ\text{C}\) with cold water: \(m_c = 150.0\,\text{g}, T_{c,i} = 20.0\,^\circ\text{C}\), \(c = 4.184\,\mathrm{J\,g^{-1}\,^\circ C^{-1}}\).
FAQs
What is specific heat capacity?
The energy required to raise 1 gram (or kilogram) of a substance by \(1^\circ\text{C}\) (or 1 K).
Do I use °C or K?
For temperature differences, \(\Delta^\circ\text{C} = \Delta \text{K}\). Ensure consistent units in calculations.
Why is my sign negative?
Exothermic cooling gives \(q < 0\); endothermic heating gives \(q > 0\). Magnitude is often reported.
Can I use this across phase changes?
No. Use latent heat \(q = mL\) for phase transitions and sum with sensible heating segments separately.
What units should I choose?
Typically, \(q\) in J, \(m\) in g, \(c\) in \(\mathrm{J\,g^{-1}\,^\circ C^{-1}}\). Convert consistently for kg/K units.
How do I handle heat losses?
Include a calorimeter constant or perform calibration runs to account for system heat capacity.
Does pressure matter?
Coffee-cup calorimetry assumes approximately constant pressure; \(q\) approximates solution enthalpy change.
Why doesn’t my mixture reach the expected temperature?
Heat losses, evaporation, or measurement errors may shift \(T_f\). Stirring and insulation reduce discrepancies.
Can I determine an unknown metal identity?
Yes. Compute \(c\) experimentally and compare with reference tables, accounting for uncertainties.
How many significant figures should I report?
Use the least precise measurement, typically 2–3 significant figures in introductory labs.
Is \(c\) temperature dependent?
For small temperature ranges, \(c\) is treated as constant; larger ranges may require temperature-dependent values.
What’s the difference between heat and temperature?
Heat \(q\) is energy transfer; temperature reflects average kinetic energy. They are related but distinct concepts.