The temperature θ°C from a candle flame is given by θ = 20 + (400/x^3) for distances x ≥ 1?
The temperature θ°C measured at a distance x cm from a candle flame is given by
θ = 20 + (400/x^3) for distances x ≥ 1
a) find the temperature gradient (i.e. the rate at which the temperature decreases with distance) 8 cm from the flame
b) Find the rate of change of temperature gradient with respect to distance, 4 cm from the flame.
Give your answers to 1 decimal place (1dp).
temperature gradient = _______________°C cm^-1 (to 1dp)
rate of change of the temperature gradient =___________________ °C cm-2 (to 1dp)
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Verified answer
θ = 20 + (400/x^3) for distances x ≥ 1
θ' = -1200/x^4
temperature gradient = - 0.3°C cm^-1 <-------
θ" = 4800/x^5
rate of change of the temperature gradient = 4.7°C cm-2 <-------