A soft drink can contains about 0.20 kg of liquid at 5 oC. Drinking this liquid can

actually consume some of the fat in the body, since energy is needed to warm the water
to body temperature (37 oC). How many kcal should the drink have so that it is in perfect
balance with the heat needed to warm the liquid.

To determine the number of kcal the drink should have to be in perfect balance with the heat needed to warm the liquid, we need to calculate the energy required to warm the liquid from 5°C to 37°C.

The specific heat capacity of liquid water is approximately 4.18 J/g°C. Since we know the mass of the liquid in the can is 0.20 kg, we can calculate the energy required using the formula:

Energy = mass x specific heat capacity x temperature change

Converting the given temperatures to Kelvin:

Initial temperature (5°C) = 5 + 273 = 278 K
Final temperature (37°C) = 37 + 273 = 310 K

Now, we can calculate the energy required:

Energy = 0.20 kg x 4.18 J/g°C x (310 K - 278 K)
= 0.20 kg x 4.18 J/g°C x 32 K
= 26.752 J

To convert Joules to kilocalories (kcal), we need to divide by the conversion factor:

1 kcal = 4184 J

Energy (kcal) = 26.752 J / 4184 J/kcal
≈ 0.006 kcal

Therefore, the soft drink should contain approximately 0.006 kcal to be in perfect balance with the heat needed to warm the liquid.

To determine the energy required to warm the liquid to body temperature, we need to calculate the heat transferred.

The heat transferred can be calculated using the formula:

Q = m * c * ΔT

Where:
Q = heat transferred (in calories or kilocalories)
m = mass of the liquid (in kilograms)
c = specific heat capacity of the liquid (in cal/g℃ or kcal/kg℃)
ΔT = change in temperature (in ℃)

In this case, the mass of the liquid is given as 0.20 kg and the change in temperature is from 5℃ to 37℃. We need to find the specific heat capacity of the liquid.

Assuming the liquid in the soft drink can is water, the specific heat capacity of water is 1 cal/g℃ or 1 kcal/kg℃.

Now, we can calculate the heat transferred:

Q = 0.20 kg * 1 kcal/kg℃ * (37℃ - 5℃)
Q = 0.20 kg * 1 kcal/kg℃ * 32℃
Q = 6.4 kcal

Therefore, the soft drink should have approximately 6.4 kcal to be in perfect balance with the heat needed to warm the liquid.

heat=mass*specificheatwater*deltatemp

solve for heat in kcal