Explanation:
Resistance R = ρL/A. Volume constant: A ∝ 1/L. Stretching length to 2L reduces area to A/2. New R' = ρ(2L)/(A/2) = 4ρL/A = 4R = 40 Ω. Resistance proportional to (length)² when volume constant.
Explanation:
Carnot efficiency η = 1 - T₂/T₁, depending solely on absolute temperatures of heat source (T₁) and sink (T₂). It is independent of working substance, engine size, or other details. This universality makes Carnot cycle the theoretical maximum efficiency benchmark. Memory tip: 'Carnot efficiency: only T_hot and T_cold matter; real engines have lower efficiency'. This thermodynamics concept is frequently tested in competitive exams. Always recall that Carnot efficiency is an ideal limit; real engines have additional losses reducing efficiency below this value.
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