Question

Be sure to answer all parts. A person drinks four glasses of cold water (3.2 degree C) every day. The volume of each glass is 2.2 times 10 mL. How much heat (in kJ) does the body have to supply to raise the temperature of the water to 37 degree C, the body temperature? How much heat would your body lose if you were to ingest 8.4 times 10^2 g of snow at 0 degree C to quench your thirst? (The amount of heat necessary to melt snow is 6.01 kJ/mol.) Enter vour answer in scientific notation.

Answer 1

Explanation:

(a). The given data is as follows.

Volume of one glass of water = $2.2 \times 10^{2}$ ml = 220 ml

Volume of 4 glass of water = $220 \times 4$ = 880 ml

We known that density of water is 1 g/ml.  Therefore, calculate the mass of water as follows.

       Mass of water = $880 ml \times 1 g/ml$

                               = 880 gm

                               = 0.88 Kg               (as 1 kg = 1000 g)

The relation between heat energy, mass and temperature change is as follows.

            Q = $mC \Delta T$

$\Delta T = (37 - 3.2)^{o}C = 33.8^{o}C$

Putting the given values into the above formula as follows.

         Q = $mC \Delta T$

             = $0.88 \times 4.186 J/g^{o}C \times 33.8^{o}C$

             = 124.5 kJ

Hence, the body have to supply 124.5 kJ to raise the temperature of the water to 37 degree C.

(b).      As we know that the heat of fusion of ice is 333 J/g.

So, energy required for $8.4 \times 10^{2}$ g or 840 g is as follows.

          $333 \times 840$ = 279.72 kJ

Heat capacity of water= 4.184 $J/g^{o}C$

Now, heat energy will be as follows.

           Q = $4.184 \times 840 g \times 37^{o}C$

               = 130.03 kJ

Therefore, total heat required = (279.72 + 130.03) kJ

                                                  = 409.75 kJ

Hence, for the given situation your body should lose 409.75 kJ  of heat.