Reference no: EM132403744

Example question and calculation:

You decided to make hot water for your favorite flavored tea drink. The water, after boiling, was at about 98 °C when you poured it over the tea bags. You now have 100 mL hot tea at 98 °C and want to dilute the tea and bring it to room temperature at about 25 °C. To make the tea to the correct temperature, you will add a portion of cold water at a temperature of 5 °C. How much cold water should you add to the hot tea water? (Hint: the density of tea and water is 1 g/mL and the specific heat of tea and water is 4.184 J/g·°C).

First convert the volume to mass using density:

100mL⋅1g1mL=100g

Next, use the following equation: q=m×C×ΔT

This problem requires an endothermic and an exothermic reaction; therefore the equation is modified: q=-q. The cold water absorbs heat and is the endothermic reaction; therefore, the cold water portion is the q. The tea temperature being brought down is releasing heat and therefore is the -q side of the equation. Now we can substitute the m×C×ΔT for each q, making sure to keep the signs of each q

(m×C×ΔT)=-(m×C×ΔT)

(m×C×(Tf-Ti))=-(m×C×(Tf-Ti))

(m×4.184Jg⋅?×(25?-5?))=-(100g×4.184Jg⋅?×(25?-98?))

(m×4.184Jg⋅?×(20?))=-(100g×4.184Jg⋅?×(-73?))

(m×83.68Jg)=-(-30,543.2J)

(m×83.68Jg)=30,543.2J

m=30,543.2J83.68Jg=365g

Convert the grams into mL with the density: 365g×1mL1g=365mL