Heat Capacity and Specific Heat
Heat capacity is C = dQ/dT for a specified process, specific heat is c = C/m, and molar heat is C_m = C/n; over a range with variable capacity the heat is the integral of C(T)dT.
Why this shows up in the exam
Choosing thermal buffers · Calorimeter water equivalents · Comparing warming rates under equal power
Learn the idea
Heat capacity measures energy needed per kelvin, while specific and molar heats normalize it by mass or amount. A large heat capacity means the same supplied energy produces a smaller temperature rise; add the heat capacities of bodies that share one temperature change.
🧠 Memory hook: Capacity belongs to the whole body; specific heat belongs to its material.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Q = m c Delta T — sensible heat for approximately constant specific heat and no phase change
- C_total = sum_i m_i c_i — combined heat capacity of bodies undergoing the same temperature change
- Q = integral_(T1)^(T2) C(T)dT — energy for temperature-dependent heat capacity
How to approach it
- 1Identify the body and thermodynamic process
- 2Convert all heat capacities to consistent units
- 3Integrate if capacity varies and then check energy dimensions
Common slip-ups that cost marks
- •Using Q=mcDelta T through a phase change
- •Mixing grams with SI specific heat
- •Treating heat capacity as independent of process for a gas
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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