Question 1

Suppose that a rigid aluminum wire were to be strung out in a loop that just fits snugly around the equator (assuming a perfectly spherical Earth with a radius of 6.37 × 10⁶ m). If the temperature of the wire is increased by 0.50°C, and the increase in length is distributed equally over the entire length, how far off the ground will the wire loop be if it remained centered on the earth? The coefficient of linear expansion of aluminum is 24 × 10^-6 K^-1. A) 7.6 mm B) 76 mm C) 76 cm D) 76 m E) 760 m

Accepted Answer

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Question 2

A 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 K^-1. A) 1.205 cm B) 1.195 cm C) 1.200 cm D) 1.210 cm

Accepted Answer

The diameter of the hole increases with temperature due to thermal expansion. The change in diameter can be calculated using the formula Δd = d0 * α * ΔT, where Δd is the change in diameter, d0 is the original diameter, α is the coefficient of linear expansion, and ΔT is the change in temperature. Here, d0 = 1.200 cm, α = 19 × 10^-6 /°C, and ΔT = 220°C - 20°C = 200°C. Thus, Δd = 1.200 * 19 × 10^-6 * 200 = 0.00456 cm. The new diameter is 1.200 cm + 0.00456 cm = 1.20456 cm, which rounds to 1.205 cm.

Question 3

For the mercury in a thermometer to expand from 4.00 cm³ to 4.10 cm³, what change in temperature is necessary? The mercury has a volume expansion coefficient of 1.80 × 10^-4 K^-1. A) 400 C° B) 140 C° C) 14 C° D) 8.2 C°

Accepted Answer

The answer of For the mercury in a thermometer to...

Question 4

A gas is taken through the cycle shown in the pV diagram in the figure. During one cycle, how much work is done by the gas? A) p₀V₀ B) 2 p₀V₀ C) 3 p₀V₀ D) 4 p₀V₀

Accepted Answer

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Question 5

A mercury thermometer has a glass bulb of interior volume 0.100 cm³ at 10°C. The glass capillary tube above the bulb has an inner cross-sectional area of 0.012 mm². The coefficient of volume expansion of mercury is 1.8 × 10^-4 K^-1. If the expansion of the glass is negligible, how much will the mercury rise in the capillary tube when the temperature rises from 5°C to 35°C if the bulb was full at 5°C? A) 0.45 mm B) 4.5 mm C) 45 mm D) 45 cm

Accepted Answer

The volume expansion of mercury can be calculated using the formula $\Delta V = V_0 \beta \Delta T$, where $\Delta V$ is the change in volume, $V_0$ is the initial volume, $\beta$ is the coefficient of volume expansion, and $\Delta T$ is the change in temperature. Given that $V_0 = 0.100 \, \text{cm}^3 = 100 \, \text{mm}^3$, $\beta = 1.8 \times 10^{-4} \, \text{K}^{-1}$, and $\Delta T = 35°C - 5°C = 30°C$, we find:$\Delta V = 100 \, \text{mm}^3 \times 1.8 \times 10^{-4} \, \text{K}^{-1} \times 30 \, \text{K} = 0.54 \, \text{mm}^3$.The height $h$ that the mercury rises in the capillary tube is given by $\Delta V = A \cdot h$, where $A = 0.012 \, \text{mm}^2$ is the cross-sectional area of the tube. Solving for $h$, we get:$h = \frac{\Delta V}{A} = \frac{0.54 \, \text{mm}^3}{0.012 \, \text{mm}^2} = 45 \, \text{mm}$.Therefore, the mercury will rise 45 mm in the capillary tube.

Question 6

An aluminum rod 17.400 cm long at 20°C is heated to 100°C. What is its new length? Aluminum has a linear expansion coefficient of 25 × 10^-6 K^-1. A) 17.435 cm B) 17.365 cm C) 0.348 cm D) 0.0348 cm

Accepted Answer

Using the formula for linear expansion: 
ΔL = αLΔT
where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.

Substituting the given values:
ΔL = (25 × 10^-6 K^-1)(17.400 cm)(100°C - 20°C)
ΔL = 0.0345 cm (rounded to four significant figures)

Adding the change in length to the original length:
New length = 17.400 cm + 0.0345 cm
New length = 17.435 cm

Therefore, the answer is A.

Question 7

A steel bridge is 1000 m long at -20°C in winter. What is the change in length when the temperature rises to 40°C in summer? The average coefficient of linear expansion of this steel is 11 × 10^-6 K^-1. A) 0.33 m B) 0.44 m C) 0.55 m D) 0.66 m

Accepted Answer

We can use the formula:

ΔL = αLΔT

where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.

Converting the temperature change to kelvin:

ΔT = 40°C - (-20°C) = 60°C = 60 K

Plugging in the values:

ΔL = (11 × 10^-6 K^-1)(1000 m)(60 K)

ΔL ≈ 0.66 m

Therefore, the answer is D.

Question 8

Two processes are shown on the pV diagram in the figure. One of them is an adiabat and the other one is an isotherm. Which process is the isotherm? 
A) process A
B) process B
C) The processes shown are neither isotherms nor adiabats.
D) It is not possible to tell without knowing if the gas is monatomic or diatomic.

Accepted Answer

The answer of Two processes are shown on the pV...

Question 9

The volume coefficient of thermal expansion for gasoline is 950 × 10^-6 K^-1. By how many cubic centimeters does the volume of 1.00 L of gasoline change when the temperature rises from 30°C to 50°C? A) 6.0 cm³ B) 12 cm³ C) 19 cm³ D) 37 cm³

Accepted Answer

We can use the formula for volume expansion:

ΔV = V₀αΔT

where:
ΔV = change in volume
V₀ = initial volume
α = volume coefficient of thermal expansion
ΔT = change in temperature

Plugging in the given values, we get:

ΔV = (1.00 L)(950 × 10^-6 /°C)(50°C - 30°C)
ΔV = 0.019 L
ΔV = 19 cm^3

Therefore, the answer is C) 19 cm^3, as this is the change in volume of the gasoline when the temperature rises from 30°C to 50°C.

Question 10

By what length will a slab of concrete that is originally 18 m long contract when the temperature drops from 24°C to -16°C? The coefficient of linear thermal expansion for this concrete is 1.0 × 10^-5 K^-1. A) 0.50 cm B) 0.72 cm C) 1.2 cm D) 1.5 cm

Accepted Answer

The length change $\Delta L$ due to temperature change can be calculated using the formula $\Delta L = \alpha L_0 \Delta T$, where $\alpha$ is the coefficient of linear expansion, $L_0$ is the original length, and $\Delta T$ is the temperature change. Here, $\alpha = 1.0 \times 10^{-5} / ^\circ C$, $L_0 = 18 m = 1800 cm$ (since 1 m = 100 cm), and $\Delta T = -16^\circ C - 24^\circ C = -40^\circ C$. Thus, $\Delta L = 1.0 \times 10^{-5} \times 1800 \times (-40) = -0.72 cm$. The contraction means the length decreases, so the change is negative, indicating a reduction in length. However, when we talk about the length by which something contracts, we refer to the absolute value, which is $0.72 cm$.

Question 11

A quantity of mercury occupies 400.0 cm³ at 0°C. What volume will it occupy when heated to 50°C? Mercury has a volume expansion coefficient of 180 × 10^-6 K^-1. A) 450 cm³ B) 409.7 cm³ C) 403.6 cm³ D) 401.8 cm³

Accepted Answer

The volume at a new temperature can be calculated using the formula for thermal expansion: $V = V_0(1 + \beta\Delta T)$, where $V_0$ is the initial volume, $\beta$ is the volume expansion coefficient, and $\Delta T$ is the change in temperature. Plugging in the given values: $400.0 \, \text{cm}^3(1 + 180 \times 10^{-6} \times 50) = 400.0 \, \text{cm}^3(1 + 0.009) = 400.0 \, \text{cm}^3 \times 1.009 = 403.6 \, \text{cm}^3$.

Question 12

The coefficient of linear expansion of steel is 12 × 10^-6 K^-1. What is the change in length of a 25-m steel bridge span when it undergoes a temperature change of 40 K from winter to summer? A) 1.2 cm B) 1.4 cm C) 1.6 cm D) 1.8 cm E) 2.0 cm

Accepted Answer

The answer of The coefficient of linear expansion of steel...

Question 13

The coefficient of linear expansion of copper is 17 × 10^-6 K^-1. A block of copper 30 cm wide, 45 cm long, and 10 cm thick is heated from 0°C to 100°C What is the change in the volume of the block? A) 2.3 × 10^-5 m³ B) 4.6 × 10^-5 m³ C) 5.2 × 10^-5 m³ D) 6.9 × 10^-5 m³ E) 14 × 10^-5 m³

Accepted Answer

The answer of The coefficient of linear expansion of copper...

Question 14

The coefficient of linear expansion of aluminum is 24 × 10^-6 K^-1 and the coefficient of volume expansion of olive oil is 0.68 × 10^-3 K^-1. A novice cook, in preparation of some pesto, fills a 1.00-L 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? A) 0.11 L B) 0.12 L C) 0.13 L D) 0.14 L E) 0.15 L

Accepted Answer

The answer of The coefficient of linear expansion of aluminum...

Question 15

A large vat contains 1.000 L of water at 20°C. What volume will this water occupy when it is heated up to 80°C? Water has a volume expansion coefficient of 210 × 10^-6 K^-1. A) 1.600 L B) 1.013 L C) 0.987 L D) 0.9987 L

Accepted Answer

The volume change due to thermal expansion can be calculated using the formula: ΔV = βV₀ΔT, where ΔV is the change in volume, β is the volume expansion coefficient, V₀ is the initial volume, and ΔT is the change in temperature. Given β = 210 × 10^-6 K^-1, V₀ = 1.000 L, and ΔT = 80°C - 20°C = 60°C, ΔV = 210 × 10^-6 × 1.000 × 60 = 0.0126 L. Therefore, the final volume is V₀ + ΔV = 1.000 L + 0.0126 L = 1.0126 L, which rounds to 1.013 L.

Question 16

The process shown on the TV graph in the figure is an 
A) adiabatic compression.
B) isothermal compression.
C) isochoric compression.
D) isobaric compression.

Accepted Answer

The process shown on the TV graph is a straight vertical line, which implies that the volume is constant. This means that there is no work being done, which happens in an isochoric process. The fact that the line is not horizontal means that the temperature is changing, so it cannot be isochoric. Additionally, the fact that the line is not sloped means that the pressure is constant, so it cannot be adiabatic or isobaric. The only process that fits these conditions is an isothermal compression.

Question 17

The process shown on the pV diagram in the figure is 
A) adiabatic.
B) isothermal.
C) isochoric.
D) isobaric.

Accepted Answer

The answer of The process shown on the pV diagram...

Question 18

The process shown on the pV diagram in the figure is an 
A) adiabatic expansion.
B) isothermal expansion.
C) isometric expansion.
D) isobaric expansion.

Accepted Answer

The answer of The process shown on the pV diagram...

Question 19

The coefficient of volume expansion of a certain olive oil is 0.68 × 10^-3 K^-1. A 1.0-L 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 L of olive oil spills over the top of the beaker. Which of the following values is closest to the coefficient of linear expansion of the glass from which the beaker is made? A) 1 × 10^-6 K^-1 B) 4 × 10^-6 K^-1 C) 1 × 10^-5 K^-1 D) 2 × 10^-5 K^-1 E) 3 × 10^-5 K^-1

Accepted Answer

First, we need to calculate the initial volume of the olive oil in the beaker. Since the beaker is filled to the brim, its volume is equal to 1.0 L. Using the coefficient of volume expansion, we can calculate the change in volume of the olive oil:
ΔV/V = βΔT
where β is the coefficient of volume expansion and ΔT is the change in temperature. Plugging in the values, we get:
ΔV/V = (0.68 × 10^-3)(25)
ΔV = 0.017 L
This is slightly larger than the amount of oil that spilled over the top of the beaker, which is 0.0167 L. This means that the volume of the beaker increased slightly due to thermal expansion. Since the beaker is made of glass, which is a relatively brittle material, it is likely that the increase in volume caused the beaker to crack slightly, allowing some of the oil to leak out.
To calculate the coefficient of linear expansion of the glass, we can use the formula:
ΔL/L = αΔT
where α is the coefficient of linear expansion and ΔL is the change in length. Since the beaker is cylindrical, we can use the formula for the volume of a cylinder to relate the change in length to the change in volume:
ΔV = πr^2ΔL
where r is the radius of the beaker. Solving for ΔL and plugging in the values, we get:
ΔL/L = ΔV/(πr^2L) = (0.0167)/(π(0.1)^2(1.0)) = 0.532 × 10^-3
This is the change in length per degree Celsius, so to get the coefficient of linear expansion, we need to divide by the temperature change:
α = ΔL/(LΔT) = (0.532 × 10^-3)/(1.0(25)) = 2.13 × 10^-5
The closest answer choice is B, 4 × 10^-6 /K.

Question 20

The coefficient of linear expansion of copper is 17 × 10^-6 K^-1. A sheet of copper has a round hole with a radius of 3.0 m cut out of it. If the sheet is heated and undergoes a change in temperature of 80 K, what is the change in the radius of the hole? A) It decreases by 4.1 mm. B) It increases by 4.1 mm. C) It decreases by 8.2 mm. D) It increases by 8.2 mm. E) It does not change.

Accepted Answer

The radius of the hole increases due to thermal expansion. The change in radius can be calculated using the formula Δr = α * r * ΔT, where Δr is the change in radius, α is the coefficient of linear expansion, r is the original radius, and ΔT is the change in temperature. Substituting the given values: Δr = 17 × 10^-6 * 3.0 * 80 = 4.08 × 10^-3 m or 4.1 mm.

Quiz 12: Thermal Properties of Matter

A 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 K-1.

For the mercury in a thermometer to expand from 4.00 cm3 to 4.10 cm3, what change in temperature is necessary? The mercury has a volume expansion coefficient of 1.80 × 10-4 K-1.

A gas is taken through the cycle shown in the pV diagram in the figure. During one cycle, how much work is done by the gas?

An aluminum rod 17.400 cm long at 20°C is heated to 100°C. What is its new length? Aluminum has a linear expansion coefficient of 25 × 10-6 K-1.

A steel bridge is 1000 m long at -20°C in winter. What is the change in length when the temperature rises to 40°C in summer? The average coefficient of linear expansion of this steel is 11 × 10-6 K-1.

Two processes are shown on the pV diagram in the figure. One of them is an adiabat and the other one is an isotherm. Which process is the isotherm?

The volume coefficient of thermal expansion for gasoline is 950 × 10-6 K-1. By how many cubic centimeters does the volume of 1.00 L of gasoline change when the temperature rises from 30°C to 50°C?

By what length will a slab of concrete that is originally 18 m long contract when the temperature drops from 24°C to -16°C? The coefficient of linear thermal expansion for this concrete is 1.0 × 10-5 K-1.

A quantity of mercury occupies 400.0 cm3 at 0°C. What volume will it occupy when heated to 50°C? Mercury has a volume expansion coefficient of 180 × 10-6 K-1.

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

The coefficient of linear expansion of copper is 17 × 10-6 K-1. A block of copper 30 cm wide, 45 cm long, and 10 cm thick is heated from 0°C to 100°C What is the change in the volume of the block?

A large vat contains 1.000 L of water at 20°C. What volume will this water occupy when it is heated up to 80°C? Water has a volume expansion coefficient of 210 × 10-6 K-1.

The process shown on the TV graph in the figure is an

The process shown on the pV diagram in the figure is

The process shown on the pV diagram in the figure is an

The coefficient of linear expansion of copper is 17 × 10-6 K-1. A sheet of copper has a round hole with a radius of 3.0 m cut out of it. If the sheet is heated and undergoes a change in temperature of 80 K, what is the change in the radius of the hole?

A 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 K^-1.

For the mercury in a thermometer to expand from 4.00 cm³ to 4.10 cm³, what change in temperature is necessary? The mercury has a volume expansion coefficient of 1.80 × 10^-4 K^-1.

An aluminum rod 17.400 cm long at 20°C is heated to 100°C. What is its new length? Aluminum has a linear expansion coefficient of 25 × 10^-6 K^-1.

A steel bridge is 1000 m long at -20°C in winter. What is the change in length when the temperature rises to 40°C in summer? The average coefficient of linear expansion of this steel is 11 × 10^-6 K^-1.

The volume coefficient of thermal expansion for gasoline is 950 × 10^-6 K^-1. By how many cubic centimeters does the volume of 1.00 L of gasoline change when the temperature rises from 30°C to 50°C?

By what length will a slab of concrete that is originally 18 m long contract when the temperature drops from 24°C to -16°C? The coefficient of linear thermal expansion for this concrete is 1.0 × 10^-5 K^-1.

A quantity of mercury occupies 400.0 cm³ at 0°C. What volume will it occupy when heated to 50°C? Mercury has a volume expansion coefficient of 180 × 10^-6 K^-1.

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

The coefficient of linear expansion of copper is 17 × 10^-6 K^-1. A block of copper 30 cm wide, 45 cm long, and 10 cm thick is heated from 0°C to 100°C What is the change in the volume of the block?

A large vat contains 1.000 L of water at 20°C. What volume will this water occupy when it is heated up to 80°C? Water has a volume expansion coefficient of 210 × 10^-6 K^-1.

The coefficient of linear expansion of copper is 17 × 10^-6 K^-1. A sheet of copper has a round hole with a radius of 3.0 m cut out of it. If the sheet is heated and undergoes a change in temperature of 80 K, what is the change in the radius of the hole?