Question 1

The coefficient of volume expansion of olive oil is 0.68 × 10^-³K^-^1.A 1-liter glass beaker is filled to the brim with olive oil at room temperature. The beaker is placed on a range and the temperature of the oil and beaker increases by 25 C°. As a result, 0.0167 liters of olive oil spill over the top of the beaker. What is the coefficient of linear expansion of glass?

Accepted Answer

The volume expansion of the oil is given by ΔV = βV₀ΔT, where β is the coefficient of volume expansion. The volume expansion of the beaker is ΔV_beaker = 3αV₀ΔT, where α is the coefficient of linear expansion of glass. The spilled volume is the difference: 0.0167 = (β - 3α)V₀ΔT. Solving for α gives α = 4 × 10⁻⁶ K⁻¹.

Question 2

A rod has a length 2.0000 m at 20.0°C. The length of the rod increases to 2.0005 m when the temperature increases to 40.0°C. What is the coefficient of thermal expansion of the material from which the rod is made?

Accepted Answer

The answer of A rod has a length 2.0000 m...

Question 3

The coefficient of linear expansion of steel is 12 × 10^-⁶K^-¹. What is the change in length of a 25-m steel bridge span when it undergoes a temperature change of 40 K?

Accepted Answer

The change in length (ΔL) can be calculated using the formula ΔL = αLΔT, where α is the coefficient of linear expansion, L is the original length, and ΔT is the temperature change. Substituting the given values: ΔL = (12 × 10^-6 K^-1)(25 m)(40 K) = 0.012 m = 1.2 cm.

Question 4

The density of water at 0°C is 999.84 kg/m³ and at 4°C it is 999.96 kg/m³. A 1.0-liter container, full to the brim with water at 4°C is placed in the refrigerator. By the time that the temperature of the water reaches 0°C, how much of the water has spilled from the container, assuming that the contraction of the container is negligible?

Accepted Answer

The answer of The density of water at 0°C is...

Question 5

The coefficient of linear expansion of lead is 29 × 10^-⁶K^-¹. What change in temperature will cause a 10-m long lead bar to change in length by 3.0 mm?

Accepted Answer

The answer of The coefficient of linear expansion of lead...

Question 6

Suppose that a steel bridge, 1000 m long, were built without any expansion joints. Suppose that only one end of the bridge was held fixed. What would the difference in the length of the bridge be between winter and summer, taking a typical winter temperature as 0°C, and a typical summer temperature as 40°C? The coefficient of thermal expansion of steel is 10.5 × 10^-⁶K^-¹.

Accepted Answer

The change in length due to thermal expansion is calculated using the formula ΔL = αLΔT. Here, α = 10.5 × 10^-6 K^-1, L = 1000 m, and ΔT = 40°C - 0°C = 40°C. Thus, ΔL = 10.5 × 10^-6 × 1000 × 40 = 0.42 m.

Question 7

1 L of water at 20°C will occupy what volume at 80°C? Water has a volume expansion coefficient of 210 × 10^-⁶/C°.

Accepted Answer

The volume expansion can be calculated using the formula: V = V₀(1 + βΔT), where V₀ is the initial volume, β is the volume expansion coefficient, and ΔT is the change in temperature. For water, V₀ = 1 L, β = 210 × 10⁻⁶/C°, and ΔT = 80°C - 20°C = 60°C. Thus, V = 1(1 + 210 × 10⁻⁶ × 60) = 1.0126 L, which is approximately 1.013 L.

Question 8

FIGURE 17-2 -A bolt hole in a brass plate has a diameter of 1.200 cm at 20°C. What is the diameter of the hole when the plate is heated to 220°C? (The coefficient of linear thermal expansion for brass is 19 × 10^-⁶ /C°.)

Accepted Answer

The diameter of the hole will increase as the plate is heated. The change in diameter can be calculated using the formula:Δd = d * α * ΔTwhere:Δd is the change in diameterd is the original diameterα is the coefficient of linear thermal expansionΔT is the change in temperaturePlugging in the given values, we get:Δd = 1.200 cm * 19 × 10^-6 /C° * (220°C - 20°C)Δd = 0.00576 cmTherefore, the new diameter of the hole will be:d + Δd = 1.200 cm + 0.00576 cmd = 1.20576 cmThe closest answer choice is A) 1.205 cm.

Question 9

FIGURE 17-2 -Two identical concrete slabs lie flat and in contact with each other as shown in Fig. 17-2. If the temperature increases by 40°C, the lower edges opposite the contact edges remained fixed in position, and the lower edges of the contact side remain in contact, at what angle φ will the slabs be tilted? The coefficient of thermal expansion of the concrete is 10 × 10^-⁶/K.

Accepted Answer

The answer of FIGURE 17-2 
-Two identical concrete slabs lie...

Question 10

A bimetallic strip is made out of two strips of metal bonded together. Each strip is 20.0 cm long and 1.00 mm thick. One strip has a coefficient of thermal expansion 4.00 × 10^-⁶/K and the other has a coefficient of thermal expansion 3.00 × 10^-⁶/K. At 20.0°C the strip is straight. What is the inner radius of curvature of the composite strip at 200°C?

Accepted Answer

The answer of A bimetallic strip is made out of...

Question 11

A bimetallic strip is made by bonding together a 1.0-mm thick and 15.0-cm long steel strip to a similar strip made of aluminum. The strip is straight when the temperature is 20.0°C. What will the radius of curvature of the strip be when the temperature is 40.0°C? The coefficient of thermal expansion of steel is 10.5 × 10^-⁶K^-¹ and that of aluminum is 23.0 × 10^-⁶K^-¹.

Accepted Answer

The radius of curvature is given by:$$R = \frac{L}{2\alpha \Delta T}$$where L is the length of the strip, $\alpha$ is the coefficient of thermal expansion, and $\Delta T$ is the change in temperature.For steel, we have:$$R_s = \frac{0.150 \ m}{2(10.5 	imes 10^{-6} K^{-1})(40.0 \ K - 20.0 \ K)} = 3.6 \ m$$For aluminum, we have:$$R_a = \frac{0.150 \ m}{2(23.0 	imes 10^{-6} K^{-1})(40.0 \ K - 20.0 \ K)} = 1.6 \ m$$The radius of curvature of the bimetallic strip is given by:$$R = \frac{R_sR_a}{R_s + R_a} = \frac{(3.6 \ m)(1.6 \ m)}{3.6 \ m + 1.6 \ m} = 2.4 \ m$$

Question 12

You want to insert an aluminum rod, which at 20°C has a radius of 1.00020 cm into a copper tube which has a radius of 1.00010 cm at the same temperature. You decide to put both of them in the refrigerator. At what temperature will the rod just fit if both are cooled to the same temperature? The coefficient of thermal expansion for aluminum is 2.4 × 10^-⁵K^-¹, and that of copper is 1.7 × 10^-⁵K^-¹.

Accepted Answer

The answer of You want to insert an aluminum rod,...

Question 13

The temperature changes from 35°F during the night to 75°F during the day. What is the temperature change on the Celsius scale?

Accepted Answer

The temperature change in Fahrenheit is 75°F - 35°F = 40°F. To convert this change to Celsius, we use the formula: (F - 32) × 5/9. However, since this is a difference in temperature, we can directly convert using 5/9 (the subtraction of 32 is not needed for differences). Thus, 40°F × 5/9 = 22.22°C, which rounds to 22°C.

Question 14

Water at room temperature of 20.0°C is poured into an aluminum cylinder which has graduation markings etched on the inside. The reading in the graduations is 300.0 cc. The cylinder with the water in it is then immersed in a constant temperature bath at a temperature of 100°C. What is the reading for the level of water on the graduations of the cylinder after the water and the cylinder reach thermal equilibrium with the bath? The volume coefficient of expansion of water is 2.07 × 10^-⁴K^-¹, and the linear coefficient of expansion of aluminum is 23.0 × 10^-⁶K^-¹.

Accepted Answer

The answer of Water at room temperature of 20.0°C is...

Question 15

A thermometer is made such that the freezing point of water is defined to be 60.0°H and the boiling point of water at sea level is defined to be 520°H. What is the Celsius temperature at 240°H?

Accepted Answer

The answer of A thermometer is made such that the...

Question 16

A student finds a blank liquid bulb thermometer and calibrates the scale by placing it in ice water and placing a reference mark at the level of the fluid. The student places the thermometer in boiling water and finds that the fluid level is 12.0 cm above the reference mark. What is the temperature when the fluid level is 2.4 cm above the reference mark?

Accepted Answer

The thermometer is calibrated such that 0 cm corresponds to 0°C (ice water) and 12 cm corresponds to 100°C (boiling water). The temperature change per cm is 100°C / 12 cm = 8.33°C/cm. At 2.4 cm, the temperature is 2.4 cm * 8.33°C/cm = 20°C.

Question 17

The Concorde's exterior is made of aluminum, which has a coefficient of linear expansion of 24 × 10^-⁶K^-¹. At 15°C, the Concorde measures 62.1 m in length. When the plane is in flight, friction with the air increases the temperature of the exterior skin to 200°C. What is the change in the length of the outer skin of the Concorde?

Accepted Answer

The answer of The Concorde's exterior is made of aluminum,...

Question 18

The volume measuring system for a gasoline pump at the service station is calibrated at 20.0°C. If the temperature of the gasoline drops to 10.0°C, what percentage extra amount of mass of gasoline do you receive when making a purchase? The coefficient of volume expansion for gasoline is 9.5 × 10^-^4/K.

Accepted Answer

The answer of The volume measuring system for a gasoline...

Question 19

The coefficient of linear expansion of aluminum is 24 × 10^-⁶K^-¹ and the coefficient of volume expansion of olive oil is 0.68 × 10^-³K^-¹. A novice cook, in preparation for deep-frying some potatoes fills a 1.00-liter aluminum pot to the brim and heats the oil and the pot from an initial temperature of 15°C to 190°C. To his consternation some olive oil spills over the top. How much?

Accepted Answer

The volume expansion of the oil is greater than the expansion of the pot. The change in volume of the oil is calculated using the formula ΔV = βV₀ΔT, and the change in volume of the pot is calculated using ΔV = 3αV₀ΔT. The difference gives the spilled oil.

Question 20

400 cm³ of mercury at 0°C will expand to what volume at 50°C? Mercury has a volume expansion coefficient of 180 × 10^-⁶/C°.

Accepted Answer

The answer of 400 cm³ of mercury at 0°C will...

Quiz 17: Temperature, Thermal Expansion, and the Ideal Gas Law

A rod has a length 2.0000 m at 20.0°C. The length of the rod increases to 2.0005 m when the temperature increases to 40.0°C. What is the coefficient of thermal expansion of the material from which the rod is made?

The coefficient of linear expansion of steel is 12 × 10-6K-1. What is the change in length of a 25-m steel bridge span when it undergoes a temperature change of 40 K?

The coefficient of linear expansion of lead is 29 × 10-6K-1. What change in temperature will cause a 10-m long lead bar to change in length by 3.0 mm?

1 L of water at 20°C will occupy what volume at 80°C? Water has a volume expansion coefficient of 210 × 10-6/C°.

FIGURE 17-2 -A bolt hole in a brass plate has a diameter of 1.200 cm at 20°C. What is the diameter of the hole when the plate is heated to 220°C? (The coefficient of linear thermal expansion for brass is 19 × 10-6 /C°.)