Heat Math Problems

Heat/Temperature Problems:

1. Suppose a piece of iron (mass = 21.50 g at a temperature of 100.° C) is dropped into an insulated container of water (mass of water = 132 g and the temperature before adding iron was 20.0° C). What will be the final temperature of the system (at thermal equilibrium)? The specific heat of iron is 0.113 cal/g° C.

2. If 200. grams of water is to be heated from 24.0° C to 100.0° C to make a cup of tea, how much heat must be added?

3. Which is more effective in cooling a drink, 10 grams of water at 0° C or 10 grams of ice at 0° C? Explain your answer quantitatively.

4. A 3.00 kg lead bar at 100.0° C is placed in 4.00 kg of water at 20.0° C. The final temperature of the lead bar would be ___________. (c_p of lead is 0.0305 cal/g° C)

5. A 0.60 kg copper kettle holds 1.70 kg of water at 30.0° C. A 0.10 kg iron ball at 120.0° C is dropped into the water. What is the final temperature of the water? (c_p of copper = 0.377 J/g° C and iron is 0.448 J/g° C)

6. A piece of iron with a mass of 20.50 grams at a temperature of 100.0° C is dropped into 140.00 grams of water at 40.0° C. What will be the final temperature of the system. The c_p of iron is 0.45 J/g° C)

7. A sample of mercury metal is heated from 25.5° C to 52.5° C. In the process, 187 cal of heat are absorbed. What mass of mercury was in the sample? The specific heat of mercury is 0.033 cal/ g° C

8. A block of aluminum weighing 140. g is cooled from 98.4° C to 62.2° C with the release of 1080 cal of heat. From these data, calculate the specific heat of aluminum.

9. A cube of gold weighing 192.4 g is heated from 30.0° C to some higher temperature, with the absorption of 226 cal of heat. The specific heat of gold is 0.030 cal/ g° C. What was the final temperature of the gold?

10. A total of 54.0 cal of heat are absorbed as 58.3 g of lead is heated from 12.0° C to 42.0° C. From these data, what is the specific heat of lead?

11. A piece of erbium metal weighing 100.0 g and heated to 95.0° C is dropped into 200.0 g of water initially at 20.0° C. The final temperature of the mixture is 21.5° C. What is the specific heat of erbium metal?

12. A block of rhenium metal (specific heat = 0.0329 cal/ g° C) is heated to 88.2° C and then dropped into 100.0 g of water initially at 26.4° C. The final temperature of the mixture is 32.4° C. What was the mass of the block of rhenium?

13. When 258.6 g of benzene vapor is condensed to a liquid at its boiling point, 33 875 cal of heat are released. What is the heat of vaporization for benzene?

14. A sample of ethyl alcohol is converted from a liquid to a vapor with no temperature change. In the process 30 640 cal of heat are absorbed. What mass of ethyl alcohol was in the sample? The heat of vaporization of ethyl alcohol is 210. cal/g.

15. The heat of combustion of methane is 212.8 kcal per mole. How much heat will be produced in the combustion of 100.0 g of methane?

16. The heat of combustion of toluene is 934.2 kcal per mole. How much heat will be released during the combustion of 250.0 g of toluene? The formula for toluene is C₆H₅CH₃

17. Copper has a density of 8.94 g/cm³ and a specific heat of 0.090 cal/g° C. A cube of copper is heated from 10.5° C to 214° C. The cube of copper has dimensions of 5.00 cm. How much heat would the copper cube absorb?

18. The specific heat of water is 4.185 J/g° C (1.00 cal/g° C). A piece of a pure metal with a mass of 24.0 g at a temperature of 45.0° C is added to 55 mL of water at 60.0° C. The final equilibrium temperature of the mixture is 95.4° C. Find the specific heat of the pure metal in both cal/g° C and J/g° C.

19. The specific heat of ice is 2.03 J/g° C. How much heat is needed to convert 550. g of ice at –15.0° C to 10.0° C?

20. What is the total amount of heat needed (in calories and joules) to convert 2.25 kg of ice at 0.0° C to steam at 200.0° C.

21. The specific heat of silicon is 0.057 cal/g° C and the density of silicon is 4.4 g/cm³. The volume of a cylinder formula is given as p r² L. The addition of 6000. calories raises the temperature of the silicon cylinder 55.5° C. Find the radius of the cylinder.

22. A piece of metal with a mass of 75.5 g is heated to 84.5° C and added to 100.0 mL of water at 5.0° C. The final temperature of the mixture is 75.0° C. Find the specific heat of the metal.

23. Granite has a specific heat of 800. J/g° C. What mass of granite is needed to store 1.50 E 6 J of heat if the temperature of the granite is to be increased by 15.5° C?

24. A 55 kg block of granite has an original temperature of 15.0° C. What will be the final temperature of this granite if 4.5 E 4 kJ of heat energy are added to the granite?