Thermodynamics

Heat is a form of energy. The unit of heat is the calorie which is the amount of heat needed to raise 1.0g of water from 14.5°C to 15.5°C. The kilocalorie (kcal) is popular and used by the food industry. Instead of kcal, the food industry uses the symbol Cal, with a large letter c so, food calories are actually kilocalories! The Joule equivalent is 1 cal = 4.2 J.

In a hot body, the particles move faster which gives them greater kinetic energy. This is what makes a hot body hot according to the kinetic molecular theory. The overall energy of motion of the particles that make up an object is called the thermal energy of that object.

The quantity of heat necessary to raise the temperature of a mass of material is

### Q = mc(Tf-Ti)

where c is the specific heatin g*°C for the material. The specific heat for water is 1.0 cal/g*°C. The specific heat of a material is the amount of energy that must be added to the material to raise the temperature of a unit mass one temperature unit. The SI units for specific heat are J/kg*K. Because one Celsius degree is equal in magnitude to one Kelvin unit, temperature changes can be measured in either Kelvin or Celsius.

**Laws of Thermodynamics**

The First Law of Thermodynamics states that thermal energy is neither created or destroyed. Energy is merely transferred from one form to another or from one object to another.

The Second Law of Thermodynamics states that natural processes go in a direction that maintains or increases the total entropy of the universe. All things will become more and more disordered unless some action is taken to keep them ordered. Entropy is a measure of the disorder in a system.

**Phase Change**

Phase changes occur when a substance goes from one state to another. For example, if water is heated from room temperature to the vapor point, it takes 1 calorie of heat (energy) to raise each gram 1 K degree. When the vapor point is reached a discrete amount of energy is required to convert each gram (or kilogram) of water at 100 °C to vapor (steam) without raising its temperature. This amount of energy is called the heat of vaporization. For water the Hv = 2.3 x 10*6 J/kg. The quantity of heat required to convert a specific amount of a liquid substance into vapor is

### Q = mHv

The **heat of fusion **is the amount of heat to change 1.0 kg of ice to liquid water at 0 °C without lowering its temperature. For water Hf = 3.3 x 10*5 J/kg. Converting a small amount of ice to water consumes a large amount of energy compared to raising the temperature of the water. It only takes 4.2 x 10*3 J/kg for each degree of temperature change with water! The quantity of heat required to convert a specific amount of a solid substance into a liquid is

### Q = mHf

**Things To Remember**

### The relationship between Fahrenheit and Celsius is F = 9/5 C + 32

### The conversion from Celsius to Kelvin is C = K - 273.1

### The relationship between changes in length, area, and volume of a substance to its change in temperature may be defined as

### Lf - Li = aLo(Tf -Ti)

### Af - Ai = gAo(Tf -Ti)

### Vf - Vi = ßVo(Tf -Ti)

### The Ideal Gas Law is represented by the equation PV = nRT, where R = 8.31 J/mol*K. To get PV = Joules, you must use Pascals and cubic centimeters. You must always use Kelvin when using the Ideal Gas Law.

**Review Question:**

1. Belinda adds 20 g of sugar (carbon) at 25 °C to a 150 g cup of coffee (water) at 80 °C. What is the final temperature of the insulated mixture? (ccarbon = 0.12 cal/g* °C)

*T = 79.1 C *

2. David takes a container holding 3 kg of water at 25 °C and adds one kilogram of ice at 0 °C. What is the the final temperature and composition (water and ice) of the mixture?

*All the ice will not be melted so the final mixture will be 3.95 kg of water and 0.05 kg of ice all at 0 degrees Celcius. There will be no further het transfer because both the water and the ice are at the same temperature. *

3. If Chris has the same container of water as David does in problem two but adds only 0.50 kg of ice, what is the final temperature of the composition?

*T = 10 C *

4. Dewayne goes over to Cassie's house for tea. Her power goes out so, he decides to heat the tea pot with a camping stove. Being a physicist, Dewayne remembers that the specific heat of copper is 0.992 cal/g* C. He then weighs the tea pot and finds it to be 1.8 kg and contains 2.0 kg of water. The water is 20 C and must be heated to 100 C. How much heat is required to heat the tea? If the stove states that it can produce 700,000 J of heat, will he be able to get the tea to boiling?

*Q = 1.73 x 10*5 cal. No, the total heat required is 728,000 J. *

5. Dan takes 40.0 g of some mysterious substance from his laboratory and finds it condenses from a vapor at 61.6 °C to a liquid at 61.6 °C. It liberates 9870 J of heat. What is the heat of vaporization of this substance?

*2.47 x 10*5 J/kg *

6. Amanda takes one of Chris's CD's and tries to melt it. Chris grabs the CD which is 100 °C and drops it into 2.00 x 10*2 g of water at 20 °C. The mass of the CD is 1.00 X 10*2 g. The water and CD reach equilibrium at 21.6 °C. What is the specific heat of the CD?

*171 J/kg*K*

7. Aklilu once again takes his 750 kg car going at 23 m/s and hits his brakes coming to a stop. The brakes contain about 15 kg of iron which absorbs the energy. What is the increase in temperature of the brakes?

*29 degrees Celsius *

8. Belinda drinks 375 ml of a soda which generates 1.7 kJ/100 ml. She decides to burn off this food energy by climbing up the stairs. How high would Belinda have to climb if she has a mass of 65.0 kg?

*1.0 x 10*1 m (about 3 flights of stairs) *

9. A 4.2 g lead bullet moving at 275 m/s strikes a steel plate and stops. If all its kinetic energy is converted to thermal energy and none leaves the bullet, what is its temperature change?

*290 degrees Celsius *

10. How much heat is added to 10.0 g of ice at -20 °C to convert to steam at 120.0 °C?

*3.09 x 10*4 J*