The pressure (in kPa) inside a sealed container is a differentiable
MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
The pressure P (in kPa) inside a sealed container is a differentiable, one-to-one function of the absolute temperature T (in K), written P=F(T). At T=400 K it is known that F′(400)=0.05 kPa/K.
(a) Describe, in complete sentences, what the value F′(400)=0.05 conveys about how the pressure is changing at T=400 K. Include units in your description.
(b) Without computing a numerical value, state whether the temperature is increasing or decreasing with respect to pressure at the instant when T=400 K. Explain your reasoning clearly.
(c) At T=400 K, a laboratory sensor reports that the temperature is rising at 0.08 K/s. Without performing any calculation beyond identifying the sign, decide whether the magnitude of dPdT is greater than, less than, or equal to 20 K/kPa at that instant. Justify your answer verbally.