Gce Model Questions Vol1 2024 Biology Question 15

At rest a human produces metabolic heat at a rate of 100 W. Heat loss to the environment occurs by conduction/radiation at a rate \(H_c = k (T_{core} - T_{amb})\) with \(k = 5\ \text{W °C}^{-1}\) and by sweating. The evaporative cooling power is \(H_s = L\,S\) where the latent heat of vapourisation \(L = 2.43\times10^{3}\ \text{J ml}^{-1}\) and the sweat rate \(S\) (ml min\(^{-1}\)) increases linearly with core temperature above 36.5 °C according to \(S = 10\,(T_{core} - 36.5)\) for \(T_{core}>36.5\) °C, otherwise \(S=0\). The ambient temperature is 30 °C, the initial core temperature is 37 °C, and the body's heat capacity is \(C = 3.5\times10^{5}\ \text{J °C}^{-1}\). Assuming the rates adjust instantly to the current core temperature, what is the core temperature after 30 min? Give your answer to one decimal place in °C.