In exercising, a weight lifter loses 0.100 kg of water through evaporation, the heat required to evaporate the water coming from the weight lifter's body. The work done in lifting weights is 1.30 x 10^5 J.
(a) Assuming that the latent heat of vaporization of perspiration is 2.42 x 10^6 J/kg, find the change in the internal energy of the weight lifter.
(b) Determine the minimum number of nutritional calories of food (1 nutritional calorie = 4186 J) that must be consumed to replace the loss of internal energy.
This is what i've done so far but I know it is wrong because I don't know where the weight of the water lost comes in.
a)
delta U = Q -W
delta U = (2.42 x 10^6) - (1.30 x 10^5)
delta U = 2290000 J
b)
if
1 cal = 4186 J
then
547.062 cal = 2290000 J
The heat loss Q is too high. You multiply 0.1 kg by 2.42 x 10^6 J/kg. That will give you a different delta U.
You did part b correctly but the question is misleading. UYse the correct delta U next time. Additional Calories are needed to maintain body heat and blood flow and other metabolic processes. The number you get will be low, so perhaps that is why they call it the minimum.
you're on the right track.. try this
Q=(.1kg)*(2.42x10^6)
delta U = -Q - W
delta U should be negative.
for part b. it's just Q/4186
To solve part a of the problem, we need to consider the change in internal energy of the weight lifter due to the loss of water through evaporation. The heat required to evaporate the water comes from the weight lifter's body, leading to a decrease in internal energy.
Now, let's calculate the change in internal energy (ΔU):
ΔU = Q - W,
where Q is the heat transferred and W is the work done.
We're given that the weight lifter loses 0.100 kg of water through evaporation. To find the heat transferred (Q), we'll use the latent heat of vaporization of perspiration, which is 2.42 x 10^6 J/kg.
Q = (mass of water lost) x (latent heat of vaporization)
= (0.100 kg) x (2.42 x 10^6 J/kg).
= 2.42 x 10^5 J.
The work done (W) is given as 1.30 x 10^5 J.
Now plug these values into the equation:
ΔU = Q - W
= (2.42 x 10^5 J) - (1.30 x 10^5 J)
= 1.12 x 10^5 J.
Therefore, the change in internal energy of the weight lifter is 1.12 x 10^5 J.
For part b, we need to find the minimum number of nutritional calories of food that must be consumed to replace the loss of internal energy.
We know that 1 nutritional calorie is equal to 4186 J.
Therefore, to find the number of nutritional calories needed, we'll divide the change in internal energy (ΔU) by the conversion factor:
Number of nutritional calories = ΔU / conversion factor
= (1.12 x 10^5 J) / (4186 J/cal)
= 26.77 cal.
So, the minimum number of nutritional calories that must be consumed to replace the loss of internal energy is approximately 26.77 cal.