Example 1 · level 1
A gas absorbs 1000 J of heat and does 600 J of work on its surroundings. Find the change in its internal energy (in J).
Show solution
- ΔU = 1000 − 600 = 400 J.
Answer: 400 J
CLASS 11–12 PHYSICS · THERMODYNAMICS
First law of thermodynamics and engine efficiency
ΔU = Q − W (Q: heat supplied to the gas, W: work done by the gas). Isobaric work W = pΔV. Carnot efficiency η = 1 − T_cold/T_hot (kelvin).
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Worked examples
Example 2 · level 2
A gas at a constant pressure of 3 × 10⁵ Pa expands by 4 L while absorbing 1800 J of heat. Find the change in internal energy (in J).
Show solution
- W = 3 × 10⁵ × 0.004 = 1200 J.
- ΔU = 1800 − 1200 = 600 J.
Answer: 600 J
Example 3 · level 3
A Carnot engine works between a hot reservoir at 327°C and a cold reservoir at 27°C. Find its efficiency in percent (correct to 2 decimal places).
Show solution
- η = 1 − 300/600 = 0.5
- = 50%.
Answer: 50