Heat Problems: 1. If you heat 50mL of water from 25C to 70C, how many calories a

Question

Heat Problems:

1. If you heat 50mL of water from 25C to 70C, how many calories are required? How many kilocalories is that?
2. If you heat 1kg of water from 0C to 50C, how many calories are required?
3. When one gram of sugar is burned in a bomb calorimeter containing 1 liter of water, the temperature of the water rises from 22C to 26C. Calculate the number of cals, kcals, and Cals in one gram of sugar.
4. When 1 gram of fat is burned in a bomb calorimeter containing 2 liters of water, the temperature rises from 21.1C to 25.8C. Calculate the number of cals, kcals, and Cals in one gram of fat. Compare the ratio of cal/gram found in fats versus sugar. (See above problem.)
5. A 12 fluid ounce can of Lite beer has a caloric content of 85 Cals. A CHE 101 student drinks an ice-cold can of this beer after a grueling chemistry exam to provide a little analgesia. The beer warms in the student’s stomach from 0C to 37C. How many cals, kcals, and Cals were required to warm the beer to body temperature?
(Hint: 16 fluid ounces = 1 pint, and one pint = 472mL.)

6. A piece of aluminum foil has a mass of 0.018g and is 5cm on each side. Given the density of aluminum as 2.7g/cc, what is the thickness of the aluminum foil in cm? In mm?
7. You have a piece of titanium foil which has a density of 4.5g/cc with a mass of 0.2g and the dimensions of 6cm X 7.4cm. What is the thickness of the titanium foil in cm? In mm?

Explanation / Answer

1. Use q = mCpdT

density of water = 1 g/ml

So, 50 ml = 50 g

q = 50 x 4.18 x (70-25) = 9405 J

q = 9.40 kJ

2. Again using q = mCpdT

q = 1000 x 4.18 x 50 = 209 kJ = 49.95 kcal

3. specific heat of sugar = 1.244 J/g.oC

using q = mCpdT

q = 1.244 x (26-22) = 4.976 J = 1.19 cal = 0.0019 kcal

Calories in 1 g of sugar = 1.19 cal/g

4. Using q = mCpdT

density of water is 1 g/ml

So 2000 ml = 2000 g

q = 2001 x 4.18 x (25.8-21.1) = 39.31 kJ = 9.39 kcal = 9390 cal

Calories per gram of fat = 9390 cal

Fat has much higher calorie content then sugar when compared.

6. density = mass/volume

So, volume = 0.018 g/2.7 g/cc = 6.67 x 10^-3 cm^3

area = 5 x 5 = 25 cm^2

thickness of aluminum foil = 6.67 x 10^-3/25 = 2.67 x 10^-4 cm

= 0.00267 mm

7. Volume of titanium foil = mass/density = 0.2/4.5 = 0.044 cm^3

area of foil = 6 x 7.4 = 44.4 cm^2

thickness of titanium foil = 0.044/44 = 0.001 cm = 0.01 mm

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