Heating Power, Losses, and Variable Thermal Response
For a lumped system with heat capacity C(T), the transient energy balance is C(T)dT/dt = P_in(t)-P_loss(T), and steady temperature occurs when input and loss powers are equal.
Why this shows up in the exam
Geysers and continuous-flow heaters · Heaters with known power loss · Inferring heat capacity from a temperature-time law
Learn the idea
Net heating power is input minus losses and equals the rate of increase of stored thermal energy. A heater may run continuously while temperature rises slowly or stops rising because some power leaks away; with variable heat capacity, the same net power gives a changing slope.
🧠 Memory hook: Input minus leakage is what warms the system.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- C(T)dT/dt = P_in-P_loss — general lumped heating balance
- P_net = m c dT/dt — constant-property sensible heating without phase change
- P_in = P_loss at steady state — thermal steady-state condition
How to approach it
- 1Choose a control mass or steady flow
- 2List every energy input and loss rate
- 3Apply the transient or steady balance and verify watts
Common slip-ups that cost marks
- •Using rated power as net power despite stated losses
- •Ignoring mass flow in a continuous heater
- •Treating a time-varying heating slope as constant heat capacity
🌟 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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