Key relationship
mhch(Th−Tf)=mccc(Tf−Tc). For ideal gases, Cp−Cv=R per mole (see gas-capacity lab).
Physics · Class 11
Mix hot and cold materials
A calorimeter balances heat lost against heat gained. A larger hot heat capacity pulls the final temperature toward the hot initial value. Specific heat has units J/(kg·K), while total heat capacity is mc.
Open the interactive experiment →Mix hot and cold materials
கலோரிமெட்ரியில் இழந்த வெப்பம் பெற்ற வெப்பத்திற்குச் சமம். மொத்த வெப்ப ஏற்புத்திறன் mc ஆகும்.
Key notes, relationships and model limits
Remember
A calorimeter balances heat lost against heat gained. A larger hot heat capacity pulls the final temperature toward the hot initial value. Specific heat has units J/(kg·K), while total heat capacity is mc.
Common trap
The final temperature is not generally the unweighted mean of initial temperatures.
Model limits
Isolated mixing, constant specific heats, negligible container heat capacity and no phase change. Pressure/volume-dependent gas heat capacities are explored separately in Kinetic Theory.
What you will learn
Balance thermal energy and compare specific heat with total heat capacity.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
For two 1 kg water samples at 80°C and 20°C, Tf=50°C and transferred heat≈1×4200×30=126000 J.
Why this matters
The model connects mix hot and cold materials with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
Mix 1 kg of water at 80°C with 2 kg at 20°C. What is Tf?
- 50°C
- 40°C
- 60°C
Read the explanation
Tf=(1×80+2×20)/3=40°C because specific heats match.
Course connection: Class XI Chapter 10. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.