Natwerk Designs

math problem???????????

A high-altitude climber is planning an ascent of Everest with new high-tech equipment. One of the innovations is a nanotechnology tent, which loses almost no energy until the temperature difference reaches 41° Fahrenheit. The climber's body puts out 55 watts while sleeping and on Everest one watt will heat ten cubic feet of air by 14° Fahrenheit per hour. If the volume of air inside the tent is 30 cubic feet, how long will it take the air inside the tent to go from Everest's nighttime temperature of zero to 41° Fahrenheit? Please round your answer to the nearest integer number of minutes now how many minutes? give me the solution thanks

Public Comments

1. Not sure if this is right, but I think that the heat transfer equation goes like this: Q = h∙V∙ΔT Where Q = heat transfer rate (Watts / hr) h = heat transfer coefficient (Watts/(hr∙ft³∙°F)) V = Volume (ft³) ΔT = change in temp (°F) So if Q=Watts / hr you can rewrite as Watts = h∙V∙ΔT∙t Where t = time in hours Okay, so we need to find the heat transfer coefficient, and we know that 1 Watt will heat 10 ft³ by 14°F in 1 hour. So sub in those values and solve for h. 1 = h (10) (14) (1) h = 1/140 Now, we know that the hiker gives off 55 Watts, and the Volume of the tent is 30 ft³, and we want to find the time it takes to get a ΔT of 41°F. So sub in all those values into our equation: 55 = (1/140)(30)(41) t And solve for t (in hours) t = 770/123 hours To get t in minutes, multiply by 60 t = 15400/41 min ≈ 375.6 minutes Answer = 376 minutes