Question

Alligators and other reptiles don't use enough metabolic energy to keep their body temperatures constant. they cool off at night and must warm up in the sun in the morning. suppose a 300 kg alligator with an early-morning body temperature of 25∘c is absorbing radiation from the sun at a rate of 1200 w. how long will the alligator need to warm up to a more favorable 30 ∘c ? (assume that the specific heat of the reptilian body is the same as that of the mammalian body.)

Answer 1

Calculating the time needed for a 300 kg alligator to warm from 25°C to 30°C with a solar absorption rate of 1200 W, the energy required is found using the specific heat formula. Time is then calculated by dividing the total energy by power, resulting in approximately 72 minutes of sun exposure.

Step-by-step explanation:

Understanding how an alligator warms up involves applying the principles of thermodynamics and energy transfer. To calculate the time it takes for the alligator to warm up, we use the specific heat formula:

Q = mcΔT

where Q is the energy in joules, m is the mass in kilograms, c is the specific heat capacity (assuming it's similar to mammals, which is approximately 3,470 J/(kg°C)), and ΔT is the change in temperature in degrees Celsius.

First, we'll find the energy required for a 300 kg alligator to warm up from 25°C to 30°C:

Q = 300 kg * 3,470 J/(kg°C) * (30°C - 25°C)

Q = 300 kg * 3,470 J/(kg°C) * 5°C

Q = 5,205,000 J

Now, knowing the alligator is absorbing solar radiation at a rate of 1200 W (watts), which is equal to 1200 J/s, we can find the time by dividing the total energy by the power:

Time (s) = Energy (J) / Power (W)

Time (s) = 5,205,000 J / 1200 W

Time (s) = 4,337.5 s

Time (min) = 4,337.5 s / 60 s/min

Time (min) = Approximately 72.29 minutes

Therefore, the alligator needs approximately 72 minutes to warm up to a favorable 30°C from an early morning body temperature of 25°C.