Question

We often use a spoon to cool coffee by stirring. Some of the heat is conducted from the coffee to the air by this method, but the spoon itself will cool the coffee a little. If a 12 gram aluminum teaspoon at 22 o C is placed in 175 ml of water (coffee's specific heat is close to water's) at 85 o C, what will the final temperature be? (Other factors, such as heat transfer to the air, may be ignored.)

Question 23 options:

78oC

92oC

84o C

82oC

Answer 1

Step-by-step explanation:

heat lost by coffee = heat gain by aluminum spoon

heat lost by coffee = mc ( 85° C - T)

175 ml of water = 175 grams

175 grams = (175 / 1000) kg = 0.175 kg

heat loss by coffee = 0.175 × 4182 J/Kgk ( 85 - T) = 731.85 ( 85-T) = 62207.25 - 731.85 T

heat gain by aluminum spoon = 0.012kg × 897 J/kgK ( T - 22) = 10.764 T - 236.808

10.764 T - 236.808 = 62207.25 - 731.85 T

10.764 T + 731.85 T = 62207.25 + 236.808

T = 84.086 ° C approx 84°C