Problem Solving Worksheet
This assignment will allow you to demonstrate the following objectives:
- Describe thermodynamic concepts and their applications.
- Extend the first law of thermodynamics to various daily life activities.
- Identify the maximum efficiency of a heat engine.
- Explain the role of latent heat while phases are changing.
Instructions: Choose 10 of the 12 problems below. Show your work. Answer the questions directly on this document.
1. The efficiency of a Carnot engine is e=1-Tc/TH, where Tc is a temperature of the cold reservoir and TH is a temperature of the hot reservoir. What is the condition to have 100% efficiency?
2. Suppose the work done to compress a gas is 100 J. If 70 J of heat is lost in the process, what is the change in the internal energy of the gas?
3. An engine's fuel is heated to 2,000 K and the surrounding air is 300 K. Calculate the ideal efficiency of the engine.
4. Mr. White claims that he invented a heat engine with a maximum efficiency of 90%. He measured the temperature of the hot reservoir as 100o C and that of cold reservoir as 10o C. Find the error that he made and calculate the correct efficiency.
5. How much energy is needed to change 100 g of 0o C ice to 0o C water? The latent heat of fusion for water L=335,000 J/kg.
6. It was determined in the 19th century that the normal human body temperature is 98.6o F. A more recent study found that it is 98.2o F. Express the difference in the temperature in Celsius.
7. Suppose 0.5 kg of blood flows from the interior to the surface of John's body while he is exercising. The released energy is 2,000 J. The specific heat capacity of blood is 4,186 J/kgo C. What is the temperature difference between when the blood arrives at the body surface and returns back to the interior of the body?
8. A student does 1,000 J of work when she moves to her dormitory. Her internal energy is decreased by 3,000 J. Determine the heat during this process. Does she gain or lose her heat?
9. A system does 100 J of work on its surroundings and gains 50 J of heat in the process. Calculate the change in the internal energy of the system and the surroundings.
10. In a construction site, 2 kg of aluminum shows the increment of temperature by 5oC. Ignoring the work, what is the change in the internal energy of the material? The specific heat capacity of aluminum is 900 J/kg oC.
11. The input heat of a Carnot engine is 3,000 J. The temperature of a hot reservoir is 600 K and that of a cold reservoir is 300 K. What is the work done?
12. A heat engine has an efficiency of 40% and yields 5,000 J of work. What are the input and output heats?