Mr. Kovall’s Neighborhood

Return to Honors Physics Home Page (revised 06-13-03)

Go to Answers to Calorimetry Problems, which also has a link to some step-by-step solutions

CALORIMETRY

SAMPLE SOLUTIONS

1. How much heat must be given up by the condensation, cooling, and freezing of 100 g of steam from 110 ^oC to ice at -15 ⁰C?

H = MC(DT) + ML_V + MC(DT) + ML_f + MC(DT)

= (100 g)(0.5 cal/g ^oC)(110 ^oC - 100 ^oC) + (100 g)(540 cal/g) + (100 g)(1 cal/g ^oC)(100 ^oC - 0 ^oC) + (100 g)(80 cal/g) + (100 g)(0.5 cal/g ^oC)[0 ^oC - (-15 ^oC)

= 500 cal + 54,000 cal + 10,000 cal + 8,000 cal + 750 cal

H = 73,250 calories = 7.325 x 10⁴ calories

2. A new temperature scale (^oN), based on the Celsius scale has just been developed where the freezing point is established at -45^o C and the

boiling point at 120^o.

(A) Derive the necessary formulas that enable one to convert between this new scale (^oN) and the Celsius scale and vice versa.

(B) Derive the temperature at which the two temperature scales are numerically the same.

N = (165/100)C - 45 C = (100/165)(N + 45) IF: ^oC = ^oN, then

C = (165/100)C - 45 and C = 69.2^o C

3. How much ice at -15^oC must be added to 150 g of steam at 110 ^oC to turn everything into water at 45 ^oC? Assume NO heat is exchanged with

any other material.

H_G = H_L

MC(DT) + ML_f + MC(DT) = MC(DT) + ML_V + MC(DT)

(x g)(0.5 cal/g^oC)[0^oC - (-15^oC)] + (x g)(80 cal/g) + (x g)(1 cal/g^oC) = (150 g)(0.5 cal/g^oC)(110^oC - 100^oC) + (150 g)(540 cal/g) + (150 g)(1 cal/g^oC)(100^oC - 45^oC)

7.5 x cal/g + 80 cal/g + 45 cal/g = 750 cal + 81,000 cal + 8,250 cal

132.5 x cal/g = 90,000 cal; x = (90,000 cal)/(132.5 cal/g)

x = 679.25 grams of ice

4. A calorimeter contains 450 g of water at 20^o C. The calorimeter has a mass of 100 g and a specific heat of 0.15 cal/g^oC. How much steam at 100^o C

is needed to raise the temperature of the water and calorimeter to 80^o C?

H_G = H_L

MC(DT) + MC(DT) = ML_v + MC(DT)

(450 g)(1 cal/g ^oC)(80 ^oC - 20 ^oC) + (100 g)(0.15 cal/g ^oC)(80 ^oC - 20 ^oC) = (x)(540 cal/g ^oC) + (x)(1 cal/g oC)(100 ^oC - 80 ^oC)

27,000 cal + 900 cal = 540(x) cal/g + 20(x) cal/g

27,900 cal = 560(x) cal/g

x = (27,900 cal)/(560 cal/g); x = 49.82 cal/g

5. How much steam at 120 ^oC must be added to 550 g of water to heat the water from 25 ^oC to 80 ^oC? Assume that NO heat is exchanged with

any other materials.

H_L = H_G

MC(DT) + ML_v + MC(DT) = MC(DT)

(x)(0.5 cal/g ^oC)(120 ^oC - 100 ^oC) + (x)(540 cal/g) + (x)(1 cal/g ^oC)(100^o C - 80 ^oC) = (550 g)(1 cal/g ^oC)(80 ^oC - 25 ^oC)

10(x) cal/g + 540(x) cal/g + 20(x) cal/g = 30,250 cal

570(x) cal/g = 30,250 cal; x = (30,250 cal)/(570 cal/g)

x = 53.1 g

PROBLEMS

NOTE: The use the following accepted values for specific heat:

Ice = 0.4995 cal/g^oC

Steam = 0.485 cal/g^oC

Specific heat values have been given in terms of cal/g^oC for convenience only. You may use J/g ^oC or J/kg^oC values, which are available in any physics or chemistry text.

1. How many calories will be liberated if 200 g of water cools from 100^o C to the freezing point and then freezes?

2. How much ice at 0^o C must be added to 2,000 g of water at 25^o C in order that the final temperature is 0^o C? Assume that NO heat is exchanged with any other materials.

3. How many calories must be absorbed to melt 80 g of lead?

(Lf = 5.7 cal/g)

4. A 200 g mass of hot copper (c = 0.093 cal/g^o C) is dropped on a large block of ice at 0^o C. As a result 210 g of ice is melted. What was the original temperature of the copper?

5. A 30 g mass of molten lead at the melting point of lead (327^o C) is dropped into 300 g of water at 15^o C. The water is held by a 15 g aluminum calorimeter. If the final temperature of the mixture is 27^o C, what is the heat of fusion of this lead sample?

6. Enough heat is supplied to 100 g of ice at 0^o C to melt the ice. If the same amount of heat that was applied to the ice, is applied to 100 g of water at 0^o C; how hot does the water become?

7. How much heat is required to evaporate 20 g of ice whose original temperature is -15^o C?

8. How much heat is given up by the condensation, cooling, and freezing of 100 g of steam? The initial and final temperatures were 100^o C and 0 ^o C respectively.

9. How much heat is required to warm 30 g of water from room temperature (20^o C) to the boiling point and then to evaporate all of it?

10. A 20 g mass of steam is condensed in 2,500 g of water at 10^o C. What is the final temperature of the mixture? No heat is lost.

11. Normal body temperature is 37^o C. Compare the amount of heat you receive from a burn due to having 10 g of boiling water spilled on your arm as compared to the amount of heat you receive from a burn due to having 10 g of steam spilled on your arm. The starting temperature of the steam and water are both100^o C.

12. How much ice must be used to cool 200 g of water from 20^o C to 0^o C? All of the ice is melted in the process.

13. The heat of vaporization of ammonia is 327cal/g. How much ammonia must be evaporated without change in temperature in a refrigerating unit to form 2 kg of ice cubes from water at 15^o C?

14. If 15 g of steam at 100^o C is condensed in a 250 g metal calorimeter (c = 0.1 cal/g^oC) that contains 100 g of ice, what will be the resulting temperature of this mixture?

15. A 150 g metal calorimeter (c = 0.1 cal/g^o C) contains 90 g of ice. If 250 g of water at 80^o C is poured over the ice, what will be the resulting temperature?

16. A 2 kg iron block (c = 0.107 cal/g^o C) at 100^o C is dropped into 750 g of water that is contained in a 325 g copper (0.093 cal/g^oC) calorimeter. If the initial temperature of the water is 12^o C, what will be its final temperature?

17. A 180 g aluminum cup (c = 0.217 cal/g^oC) contains 400 g of water, all at 25^o C. How many calories are required to raise their temperature of 100^o C?

18. Lead shot (c = 0.306 cal/g^oC) weighing 800 g at 100^o C is dropped into a 280 g brass (c = 0.089 cal/g^oC) calorimeter cup that contains 350 g of water. If the initial temperature of the water was 15^o C, what will be the resulting temperature?

19. A 450 g cylinder at 150^o C is dropped into 200 g of water at 15^o C. The water is contained in a 200 g brass calorimeter (c = 0.089 cal/g^o C) and the resulting water temperature is 39^o C. What is the specific heat of the cylinder?

20. A small crucible contains 300 g of gold (c = 0.032 cal/g^oC) is heated to the temperature of a small furnace. The gold is then dropped into 1 kg of water at 10^o C. If the water temperature rises to 20^o C, what was the temperature of the furnace?

21. A 0.75 kg block of metal at 100^o C is dropped into a 50 g copper (c = 0.093 cal/g^oC) calorimeter cup which contains 0.56 kg of water at 20^o C. If the final temperature reached is 30^o C, what is the specific heat of the sample?

22. A 2 kg block of metal at 100^o C is dropped into the cavity of a large block of ice at 0^o C. If 268 g of ice is melted, what is the specific heat of the metal?

23. Let 800 g of lead (c = 0.306 cal/g^oC) at 90^o C and 300 g of copper (c = 0.093 cal/g^oC) at 100^o C be dropped into a 100 g copper calorimeter containing 500 g of water at 15^o C. What is the resultant temperature?

24. A 105 g aluminum calorimeter (c = 0.217 cal/g^oC) contains 250 g of water at 25^oC. Find the final temperature of the mixture when 600 g of copper (c = 0.093 cal/g^oC) at 98^o C is placed in the water?

25. Consider the calorimeter in problem #24 is made of 105 g of copper and that the 600 g of aluminum is heated to 98^o C is added to the water. What would be the resulting temperature. (All specific heats remain the same.)

26. If 100 g each of lead shot (c = 0.031 cal/g^oC) at 80^o C, water at 30^o C, and ice at 0^o C are mixed together without loss of energy, what will be the resultant temperature, and how much ice will be melted?

27. A 0.150 kg copper calorimeter (c = 0.93 cal/g^oC) contains 375 g of water at 20^o C. Into this we place 250 g of lead (c = 0.306 cal/g^oC) at 95^o C and 100 g of aluminum (c = 0.217 cal/g^oC) at 50^o C. What is the resulting temperature?

28. A 0.75 dkg copper calorimeter (c = 0.093 cal/ ^oC) contains 1.75 g of water at 64^o C. When 50 g of a metal at 18^o C is added, the resulting temperature is 24^o C. What is the specific heat of the metal sample?

29. When 0.55 kg of a metal sample is heated to 100^o C and is then placed on a large cake of ice, 0.105 kg of the ice melted. What is the specific heat of the metal?

30. A 225 g aluminum calorimeter (c = 0.217 cal/g^oC) contains 300 g of water at 20^o C. Into this we place 250 g of iron (c = 0.115 cal/g^oC) at 150^o C and 20 g of ice at -10^o C. What is the final temperature of the mixture?

31. A 150 g copper calorimeter (c = 0.093 cal/g^oC) contains 250 g of water at 35^o C. Into the water we place 100 g of ice at -12^o C. What is the resulting temperature?

32. A 10 g mass of lead cools from 342^o C to the fusion point (327^oC) in 1.95 minutes. After which, the temperature remains constant for 21.1 minutes while the mass solidifies. Consider that the rate of heat loss is uniform and that the specific heat of lead above 327^o C is 0.036 cal/g^oC. What is the latent heat of fusion of this lead.

33. A 200 g piece of lead is heated to 100^o C and is then dropped into 100 cc of water at 4.5^o C. If the final temperature is 10^o C, what is the specific heat of this lead?

34. If 400 g of aluminum (c = 0.217 cal/g^oC) at 220^o C is dropped into 300 g of water at 10^o C which is contained in a 100 g copper calorimeter (c = 0.093 cal/g^oC), what is the resulting temperature?

35. How many grams of ice are needed to reduce the temperature of 3 kg of boiling water from 100^o C to 10^o C?

36. How many grams of ice at -15^o C can be melted by 5 g of steam at 105^o C, if the resulting temperature of the mixture is 0^o C?

37. Ten grams of steam at an unknown temperature above 100 ° C are mixed with 200 g of water at 25^o C in a 50 g aluminum calorimeter (c = 0.214 cal/g^oC). If the resulting temperature is 53.1 ^o C, what is the original temperature of the steam?

38. Eight grams of steam are passed into 225 g of water at 15^o C which is contained in an 85 g copper calorimeter (c = 0.093 cal/g^oC). If the final temperature is 35.6^o C, what is the latent heat of this steam?

39. What is the result when 10 g of steam is added to 50 g of ice?

40. A 340 g aluminum pan (c = 0.214 cal/g^oC) is placed on a stove at 4:05 P.M. The pan contains 300 g of water at 20^o C. The flame under the pan supplies 100 cal of heat to the system each second. What time of day will the clock indicate when the:

(A) water begins to boil?

(B) the pan and its contents begin to rise above 100^o C?

41. How much steam at 110^o C would have to be added to 60 g of ice at 0^o C for the equilibrium temperature to be 40^o C?

42. A 2,000 g copper ball is heated to 700^o C and is then placed on a large block of ice. What is the end result?

43. A 60 g ice cube at -10^o C is dropped into a beaker of water at 0^o C. How much water will freeze onto the ice cube?

44. How much heat must be liberated to change 15 g of steam at 120^o C to ice at -40^o C?

45. What is the final temperature attained when 900 g of ice at -5^o C is dropped into 3,400 g of water at 95^o C in a 1,350 g calorimeter whose specific heat is 0.090 cal/g^oC?

46. A 50 g brass ball (c = 0.092 cal/g^oC) is placed in a 100 g aluminum calorimeter (c = 0.214 cal/g^oC) with 250 g of water at 20^o C. What equilibrium temperature is reached upon the addition of 25 g of steam at 125^o C?

47. How much heat s liberated when 250 g of steam at 140^o C is converted into ice at -20^o C?

48. In an experiment to determine the heat of vaporization of water, 14 g of steam at 100^o C is added to 150 g of water at 22^o C in a 76 g calorimeter (c = 0.2 cal/g^oC). If the equilibrium temperature reached is 75^o C, what is the experimental value for the heat of vaporization? Include the percentage error, where the accepted value is 539 cal/g.

49. A 100 g calorimeter (c = 0.100 cal/g^oC) contains 400 g of water at 20^o C. How many grams of steam at 100^o C are required to raise the temperature of the mixture to 80^o C?

50. In an experiment to determine the heat of vaporization of water, 15 g of steam at 100^o C are added to 150 g of water at 20^o C. The water is contained in a 75 g calorimeter (c = 0.1 cal/g^oC). The equilibrium temperature reached is 73.9^o C.

(A) What is the heat of vaporization of this sample of water?

(B) What would be the per cent error of this experiment?

51. A 50 g aluminum cylinder is placed in a 100 g brass calorimeter (c = 0.89 cal/g^oC) which also contains 250 g of water at 20^o C. 25 g of steam at 120 ^o C are introduced to the mixture. If the resulting equilibrium temperature is 62 ^o C, what is the experimental value for the specific heat of the aluminum cylinder. Include the percentage error, where the accepted specific heat for aluminum is 0.217 cal/g ^oC.

52. If you had a Centigrade thermometer and an unmarked thermometer for which you had just found the boiling and freezing points. You labeled the freezing point of the unmarked thermometer as -20^o and the boiling point as 180^o. Knowing that the boiling and freezing points on the Centigrade scale are100^o C and 0^o C respectively, derive the following:

(A) The conversion formulas that would enable you to convert from the Centigrade scale to the unmarked scale.

(B) The conversion formulas that would enable you to convert from the unmarked scale to the Centigrade scale.

(C) The temperature where both the Centigrade and the unmarked scale would read numerically the same?

53. In a Physics experiment, a student immersed 100 copper pennies (3.0 g each) in boiling water which is being heated over a Bunsen burner. After they reached thermal equilibrium with the water, they were taken out an immediately placed into 0.2 kg of water at 20^o C. What was the final temperature of the water and the pennies? (C_Cu = 390 Joule/Kg^oC; C_water = 4186 Joule/kg^oC)

54. You are given a glass container which you are requested to heat through 65^o C; but, you were given a Fahrenheit thermometer by mistake. Through what Fahrenheit degrees would you have to work?

55. If you had a Centigrade thermometer and an unmarked thermometer for which you had just found the boiling and freezing points. You labeled the freezing point of the unmarked thermometer as -120^o C and the boiling point as 180^o C. Knowing that the boiling and freezing points on the Centigrade scale are 100^o and 0^o respectively, derive the following:

(A) The conversion formulas that would enable you to convert from the Centigrade scale to the unmarked scale.

(B) The conversion formulas that would enable you to convert from the unmarked scale to the Centigrade scale.

(C) The temperature where both the Centigrade and the unmarked scale would read numerically the same?

SELF-TEST

Multiple Choice

1. When heated, most materials:

(A) expand (C) bend

(B) contract (D) solidify

2. Heat travels through solids mainly by:

(A) radiation (C) convection

(B) conduction (D) expansion

3. The BEST insulator against the conduction of heat is:

(A) air (C) silver

(B) asbestos (D) a vacuum

4. A thermometer reading 68^o Fahrenheit is equal to a reading of:

(A) 12^o Kelvin (C) 36^o C

(B) 20^o C (D) 68^o Kelvin

5. The temperature of a body can always be increased by increasing:

(A) its volume (C) the energy of its molecules

(B) its mass (D) the size of its molecules

6. If a piece of copper is placed in water, heat must go from the:

(A) water to the copper (C) water to the copper to the air

(B) copper to the water (D) the warmer substance to the colder

7. A warm humid day is less comfortable than a warm dry day because the high humidity decreases:

(A) evaporation (C) circulation

(B) condensation (D) absorption

8. Lightning is produced by the build-up of electric charges as:

(A) rain droplets split (C) hail falls

(B) water droplets freeze (D) water vapor condenses

9. The zigzag movement of smoke particles resulting from their collisions with air molecules is:

(A) Brownian movement (C) a bonding force

(B) Celsius movement (D) an adhesion force

10. Some aluminum pots have wooden handles because wood is:

(A) a good conductor (C) lighter than aluminum;

(B) a poor conductor (D) heavier than aluminum.

11. On a summer day, a person would be warmest if dressed in:

(A) white (C) yellow

(B) black (D) lavender

12. The Earth’s atmosphere is heated by:

(A) radiation (C) conduction

(B) convection (D) all of the above

13. Thunderstorms usually occur when the air is:

(A) cool and moist (C) warm and moist

(B) cool and dry (D) warm and dry

14. The force of cohesion can cause water to:

(A) form drops (C) spread on tile

(B) evaporate (D) wet unpainted surfaces

15. The uneven expansion of metals is the basis for the operation of the:

(A) alcohol thermometer (C) vacuum bottle

(B) mercury thermometer (D) thermostat

16. Gases are good insulators because:

(A) they prevent convection currents (C) their molecules move slowly

(B) their molecules are far apart (D) they cannot be compressed

17. As warm air pushes over stationary or slower moving cold air:

(A) a warm front forms (C) a hurricane forms

(B) a cold front forms (D) a static front forms

18. If the air at 80^o F holds only 40% of the water vapor it can hold, the relative humidity is:

(A) 20% (C) 60%

(B) 40% (D) 80%

19. If you “seed” with silver iodide crystals, a cloud whose relative humidity is above 100%, snow may result as the crystals:

(A) cool the cloud (C) provide a center on which moisture condenses

(B) warm the cloud (D) increases the moisture in the cloud

20. A change in Centigrade temperature from 0^o to100^o would be the same as a change in Fahrenheit temperature from:

(A) 20^o to 100^o (C) 32^o to 100^o

(B) 20^o to 220^o (D) 32^o to 212^o

21. As the cool refrigerating gas moves in the coils of the ice tray compartment of a refrigerator, the gas:

(A) gives off heat (C) becomes cooler

(B) takes in heat (D) contracts

22. Along the seashore at night, there are usually:

(A) thunderheads (C) sea breezes

(B) lightning flashes (D) land breezes

23. If one liter of gas at 0^o C is heated to 237^o C, its volume becomes:

(A) 1/2 liter (C) 2 liters

(B) 1 liter (D) 4 liters

24. You are most comfortable when the air around you has a relative humidity of :

(A) 40% and a temperature of 86^o F (C) 68% and a temperature of 50^o F

(B) 50% and a temperature of 68^o F (D) 86% and a temperature of 40^o F

25. If you want your house to be easy to heat in the winter, DO NOT use:

(A) an overhang above the windows (C) double-layer window glass

(B) silver paint on the radiators (D) insulation in the walls

26. On the western slopes of the Rocky Mountains, rain may fall as the warm air:

(A) contracts and cools (C) rises and cools

(B) contracts and becomes warmer (D) rises and becomes warmer

27. Hammering a nail or rubbing two pieces of metal together produce heat by causing:

(A) molecules to move faster (C) contraction;

(B) molecules to move slower (D) expansion.

28. As fuel is burned in a furnace:

(A) heat is changed to chemical energy (C) electrical energy is changed to heat

(B) chemical energy is changed to heat (D) heat is changed into electrical energy

29. A good air conditioner controls:

(A) temperature and precipitation (C) heating and moisture

(B) cooling and heating (D) temperature and humidity

30. A vacuum bottle is double-walled to prevent heat loss by:

(A) evaporation (C) conduction

(B) reflection (D) condensation

31. At the temperature of absolute zero, there:

(A) is no molecular motion (C) are no molecules

(B) is much molecular motion (D) is some heat

32. Heat transfer between two bodies occurs when one of the bodies:

(A) is at a higher temperature (C) is a better conductor of heat

(B) one has a larger specific heat (D) has a greater heat capacity

33. When the condenser coils of your refrigerator at home feel warm, one should normally:

(A) turn off the refrigerator and call the repairman

(B) defrost the refrigerator

(C) be assured that the refrigerator is operating properly

(D) assume that the food would spoil inside the warm refrigerator

34. As ice melts, its temperature:

(A) rises (C) remains constant

(B) falls (D) may rise or fall depending on the surroundings

35. The change of state from a solid to a liquid is called:

(A) vaporization (C) fusion

(B) sublimation (D) solidification

36. Actual cooling inside an electric refrigerator is brought about by:

(A) condensation (C) compression

(B) evaporation (D) electricity

37. If 10 g of steam at 120^o C is added to 500 g of water at 0^o C, the final temperature of the mixture is:

(A) 4.6^o C (C) 38.1^o C

(B) 12.8^o C (D) 59.3^o C