Question

what is the temperature after 55 minutes? when will its temperature be 17 degrees celsius

Round your answers to two decimal places. when a cold drink is taken from a refrigerator, its temperature is Sec. After 25 minutes in a 20C room its temperature has in reased to 10 C (e) What is the temperature of the drink after 5S minutes? "С (b) When will its temperature be 17 C? Submt Answer Save Progress <c View Previous Question Question 9 of 25 View Next Quesion

Answer 1

Write the equation for Newton's law of cooling as follows dT = k(20-7) dt Here, k is the proportionality constant, 20 is the room temperature and Tis thetemperature Intergrate on both sides a(20-7) 20-T -in(20-7)= it-Inc 20-T 20-T -k 20-T-ce Initially the temperature is 5 °C, t = 0 Substitute Ofor t and 5 Cfor Tin equation (1) 20-5- ce-0) Afetr 25 min, the temperatureis 10 °C Substitute 15 for e,25 minfor t and 10 Cfor Tin equation (1) 20-T = ce 20-10- 15xe-*S»n) -0.667 -(25 min)n (0.667) t= 0.405 -25 min k= 0.0162 min-1

Given t 55 min Substitute 15 for c,55 min for t and 0.0162 min for k in equati on (1) 20-T-ce 20-T= 15xe 20-T- 6.15 T= 20-615°C T- 13.85 °C Therefore, the required temperature is 13.85°C 0.0162m'x5Smini т-17 °C Substitute 15 for c,17°Cfor T and 0.0162 min for kin equati on (1) 20-T = ce 20-17- 15xe-001mh' 0.0162minxt ×e -0.0162mm"'xt= 0.2 -0.0162 min-ıxz=-1.609 1.609 0.0162 min t99.32 min Therefore, the required time is 99.32 min