Question

A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 8.10kg of water at 33.9 degrees celsius . During the reaction 69.0kJ of heat flows out of the bath and into the flask.
Calculate the new temperature of the water bath. You can assume the specific heat capacity of water under these conditions is 4.18J*g*K. Round your answer to 3 significant digits.

Answer 1

Explanation:

The given data is as follows.

        q = 69.0 kJ = 69000 J (as 1 kJ = 1000 J),

       mass (m) = 8.10 kg = 8100 g  (as 1 kg = 1000 g)

        $T_{i} = 33.9^{o}C$ = (33.9 + 273) K = 306.9 K

         C = 4.18 J/gK

As we know that the relation between heat and change in temperature is as follows.

                   q = $m \times C \times \Delta T$

Putting the values into the above formula to calculate the final temperature as follows.

                  q = $m \times C \times \Delta T$

       69000 J = $8100 g \times 4.18 J/g K \times (T_{f} - 306.9 K)$                

           69000 J = $33858 \times (T_{f} - 306.9 K)$

                  $(T_{f} - 306.9 K)$ = 2.037 K

                    $T_{f}$ = (2.037 + 306.9) K

                                  = 308.9 K

or,                               = 309 K (approx)

Thus, we can conclude that the new temperature of the water bath is 309 K.