Igcse Model Questions Vol1 2023 Biology Question 26

A resting adult produces metabolic heat at a rate of \(100\;\text{W}\). Heat loss to the environment occurs by convection and radiation and is proportional to the temperature difference between the body core and the ambient air: \(\dot Q_{\text{loss}} = k\,(T_{\text{body}}-T_{\text{amb}})\). Initially the proportionality constant is \(k = 5\;\text{W/°C}\) and the ambient temperature is \(20^{\circ}\text{C}\). The combined mass and specific heat capacity of the body is \(C = 3500\;\text{J/°C}\).\n\n(a) If the body temperature is initially \(37^{\circ}\text{C}\), how many minutes will it take for the core temperature to rise to \(38^{\circ}\text{C}\) assuming no sweating?\n\n(b) When the core temperature reaches \(38^{\circ}\text{C}\) the person begins light exercise, raising the metabolic heat production to \(150\;\text{W}\) while \(k\) remains \(5\;\text{W/°C}\). Assuming the ambient temperature is unchanged, how many additional minutes are required for the temperature to rise from \(38^{\circ}\text{C}\) to \(39^{\circ}\text{C}\)?