A person falls in water at 0 C. After 30 min in the water, he/she suffers from hypothermia, as their body temp drops to 30 C. Since we are water.... we assume the heat capacity is 4.18 J/g/C. 180 Kcal of energy is required to raise the persons temp to 40 C. I need to find the mass.
You use Q=mc dT but I'm confused about temperature?
I also know that 180 kcal is 753 120 J.
What do we use for dT.. is it 40-30?
The heat capacity 0f 4.18 J/g.ºC is equivalent to 1.00 cal/g.ºC or 1.00kcal/kg.ºC
180kcal = (1.00kcal/kg.ºC)(m)(10.0ºC)
Solve for m
sweet thanks GK!
To find the mass of the person, you can use the formula Q = mcΔT, where Q is the amount of heat transferred, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
In this case, we know that 180 kcal is equal to 753,120 J, so Q = 753,120 J. The specific heat capacity for water is 4.18 J/g/°C, and the change in temperature is the final temperature (40°C) minus the initial temperature (30°C), so ΔT = 40°C - 30°C.
Since we are dealing with water in this scenario, we can assume that the mass refers to the mass of water. Thus, now you can rearrange the formula and solve for m:
Q = mcΔT
753,120 J = m * 4.18 J/g/°C * (40°C - 30°C)
Now, plug in the known values:
753,120 J = m * 4.18 J/g/°C * 10°C
Simplify the equation:
753,120 J = m * 41.8 J/g
753,120 J / 41.8 J/g = m
Divide the values:
m ≈ 18,042 g
Therefore, the mass of the person is approximately 18,042 grams (or 18.042 kg).