Supplementary Topic: Specific Heat

SUPPLEMENTARY TOPIC: SPECIFIC HEAT 1 Supplementary Topic: Specific Heat Why is the climate in a coastal city often more moderate than that of a city located 100 miles inland? To answer a question of this sort, we must understand the concept of specific heat, a physi property that relates energy, mass, and temperature change. The specific heat is a measure of how much heat a substance must absorb to increase its temperature a given amount. The specific heat is the amount of heat energy (in ories or joules) needed to raise the temperature of 1 g of a substance by 1 C. specific heat heat mass ΔT (OR J) 1 g 1 C The specific heat of water is 1.00 /(g C), meaning that 1.00 of heat must be added to increase the temperature of 1.00 g of water by 1.00 C. The amount of heat that must be added for a particular temperature increase depends on the amount of sample present. To increase the temperature of 2.00 g of water by 1 C requires 2.00 of heat. Table 1 lists the specific heat values for a variety of substances. The larger the specific heat of a substance, the less its temperature will change when it absorbs a particular amount of heat energy. The specific heat of graphite is about twice that of copper. Adding 1.00 of heat will raise the temperature of 1.00 g of graphite by 5.9 C, but raise the temperature of 1.00 g of copper by 11.1 C. Because metals like copper have low specific heats, they absorb and transfer heat readily. We use copper, iron, or aluminum cookware because the metals readily transfer heat from the stove to the food in the pan. The specific heat of water is very high compared to other liquids. As a result, water absorbs a large amount of heat with only a small change in temperature. Moreover, since the amount of heat absorbed for a given temperature increase equals the amount of heat released upon cooling, water releases a great deal of energy when its temperature drops even a few degrees. A large body of water thus acts as a reservoir to absorb or release heat as temperature increases or decreases, and in this way, it moderates the climate of the land nearby. Table 1 Specific Heats of Some Substances Substance /(g C) J/(g C) Substance /(g C) J/(g C) Aluminum 0.214 0.895 2-Propanol 0.612 2.56 Carbon (graphite) 0.169 0.707 Rock 0.200 0.837 Copper 0.0900 0.377 Sand 0.200 0.837 Ethanol 0.583 2.44 Silver 0.0560 0.234 Gold 0.0310 0.130 Water(l) 1.00 4.18 Iron 0.107 0.448 Water(g) 0.481 2.01 Mercury 0.0335 0.140 Water(s) 0.486 2.03

2 SUPPLEMENTARY TOPIC: SPECIFIC HEAT SAMPLE PROBLEM 1 Consider the elements aluminum, copper, gold, and iron in Table 1. (a) If 10 k of heat is added to 10 g of each element, which element will have the highest temperature? (b) Which element would require the largest amount of heat to raise the temperature of a 5-g sample by 5 C? The larger the specific heat, the less the temperature of a substance will change when it absorbs heat energy. The larger the specific heat, the more heat that must be added to increase the temperature of a substance a given number of degrees. The specific heats of the metals in Table 1 increase in the following order: gold < copper < iron < aluminum. In part (a), gold has the lowest specific heat, so its temperature will be the highest if the same amount of heat is added to the same mass of all four elements. In part (b), aluminum has the largest specific heat, so it will require the largest amount of heat to raise its temperature the same number of degrees as the same mass of the other elements. PROBLEM 1 A student has two containers one with 10 g of sand and one with 10 g of ethanol. (a) Which substance has the higher temperature after 10.0 of heat is added to each container? (b) Which substance requires the larger amount of heat to raise its temperature by 10 C? PROBLEM 2 The human body is composed of about 70% water. How does this help the body to maintain a steady internal temperature? We can use the specific heat as a conversion factor to culate how much heat is absorbed or lost from a substance as long as its mass and change in temperature are known, using the equation: heat absorbed or released heat mass temperature change specific heat ΔT g C g 1 C Sample Problem 2 shows how to use specific heat to culate the amount of heat absorbed by a substance when the mass and temperature change are known. SAMPLE PROBLEM 2 How many ories are needed to heat a pot of 1,600 g of water from 25 C to 100. C? Use specific heat as a conversion factor to culate the amount of heat absorbed using the known mass and temperature change. [1] Identify the known quantities and the desired quantity. mass 1,600 g T 1 25 C T 2 100. C known quantities? ories desired quantity Subtract the initial temperature (T 1 ) from the final temperature (T 2 ) to determine the temperature change: T 2 T 1 T 100. 25 75 C. The specific heat of water is 1.00 /(g C).

SUPPLEMENTARY TOPIC: SPECIFIC HEAT 3 [2] Write the equation. The specific heat is a conversion factor that relates the heat absorbed to the temperature change ( T) and mass. heat mass T specific heat g C g C [3] Solve the equation. Substitute the known quantities into the equation and solve for heat in ories. 1600 g 75 C 1.00 1 g 1 C 1.2 10 5 Answer PROBLEM 3 How much energy is required to heat 28.0 g of iron from 19 C to 150 C? Report your answer in ories and joules. PROBLEM 4 How much energy is released when 200. g of water is cooled from 55 C to 12 C? Report your answer in ories and kiloories. Building on what you have learned in Sample Problem 2, Sample Problem 3 shows how to determine the temperature change of a given mass of a substance when the amount of heat absorbed is known. SAMPLE PROBLEM 3 If 400. of heat is added to 25.0 g of 2-propanol at 21 C, what is the final temperature? 2-Propanol is the major component of rubbing alcohol, which is used to clean skin before suturing. Use specific heat as a conversion factor to determine the temperature change ( T) given the known mass of the substance and the amount of heat absorbed. Add the temperature change to the initial temperature (T 1 ) to obtain the final temperature (T 2 ). [1] Identify the known quantities and the desired quantity. mass 25.0 g heat added 400. T 1 21 C T 2? known quantities desired quantity According to Table 1, the specific heat of 2-propanol is 0.612 /(g C). [2] Write the equation and rearrange it to isolate T on one side. Divide both sides of the equation by mass (in g) and specific heat [in /(g C)] to place T (in C) on one side. heat mass T specific heat heat mass specific heat g /(g C) T T

4 SUPPLEMENTARY TOPIC: SPECIFIC HEAT [3] Solve the equation to determine the change in temperature. T g /(g C) 400. 25.0 g 0.612 /(g C) 26.1 C temperature change [4] Add the change in temperature ( T) to T 1 obtain the final temperature T 2. PROBLEM 5 21 + 26.1 47 C T 2 final temperature If 20. of heat is added to 10.0 g each of copper and mercury at 15 C, what is the final temperature of each element? PROBLEM 6 If the initial temperature of 120. g of ethanol is 20. C, what will be the final temperature after 950. of heat is added? Additional Problems PROBLEM 7 The same amount of heat is added to the same mass of two compounds X and Y at the same initial temperature. If the final temperature of X is higher than the final temperature of Y, how do the specific heats of X and Y compare? PROBLEM 8 If it takes 37.0 of heat to raise the temperature of 12.0 g of a substance by 8.5 C, what is its specific heat? PROBLEM 9 How much energy is absorbed or lost in each of the following? Calculate your answer in both ories and joules. a. the energy needed to heat 50. g of water from 15 C to 50. C b. the energy lost when 250 g of aluminum is cooled from 125 C to 50. C PROBLEM 10 How many ories of heat are needed to increase the temperature of 55 g of ethanol from 18 C to 48 C? PROBLEM 11 Which of the following samples has the higher temperature? a. 100. g of liquid water at 16.0 C that absorbs 200. of heat b. 50.0 g of liquid water at 16.0 C that absorbs 350. J of heat PROBLEM 12 Which has the higher final temperature, 10.0 g of aluminum at 18 C that absorbs 25.0 of heat or 12.0 g of iron at 22 C that absorbs 65.0 J of heat? PROBLEM 13 Why does it take weeks for a lake to freeze in the winter even if the outdoor temperature is consistently below 0 C?

SUPPLEMENTARY TOPIC: SPECIFIC HEAT 5 PROBLEM 14 Consider the following three containers (A C) drawn below. (a) If the same amount of heat was added to all three samples, which sample has the highest temperature? (b) Which sample has the lowest temperature? ethanol ethanol 2-propanol A B C Challenge Problem PROBLEM 15 How much heat (in k) must be added to raise the temperature of the water in a 400.-gal hot tub from 60. F to 110. F? (Rel that the density of water is 1.00 g/ml.)