Q: A metal rod of length $$L = 2.0\ \mathrm{m} is $$heated from $$20\ ^\circ\mathrm{C} to$$ $$80\ ^\circ\mathrm{C}. If $$the coefficient of linear expansion is $$\alpha = 1.2 \times 10$$^{-5}$$\ \mathrm{K}^{-1}$$, what is the change in length?

$$\Delta L = \alpha L \Delta T = 1.2 \times 10$$^{-5}$$ \times 2.0 \times (80 - 20) = 1.44 \times 10$$^{-3}$$\ \mathrm{m}$$

Q: A copper flask ($$\alpha = 17 \times 10$$^{-6}$$\ \mathrm{K}^{-1}) $$with a volume of $$201\ \mathrm{cm}^3 is $$filled to the brim with olive oil ($$\beta = 0.68 \times 10$$^{-3}$$\ \mathrm{K}^{-1}). If $$the temperature increases from $$11\ ^\circ\mathrm{C} to$$ $$36\ ^\circ\mathrm{C}$$, how much oil spills from the flask?

$$\Delta V = V_0$ (\beta - 3\alpha) \Delta T = 201 \times (0.68 \times 10$$^{-3}$$ - 3 \times 17 \times 10$$^{-6}$$) \times 25 = 3.06\ \mathrm{cm}^3$$

Question 1

Which of the following statements best describes the concept of 'heat' as used in thermodynamics?

Accepted Answer

Heat is the energy that is transferred between objects because of a temperature difference.

Question 2

A scientist measures the temperature of a substance as 25 ºC. What is this temperature in Kelvin?

Accepted Answer

$$T_K = T_C + 273.15 = 25 + 273.15 = 298.15\ \mathrm{K}$$

Question 3

Which of the following is the correct formula to convert a temperature from Fahrenheit to Celsius?

Accepted Answer

$$T_C = \frac{5}{9}(T_F - 32)$$

Question 4

On a brisk winter morning, the temperature is $$-2\ ^\circ\mathrm{C}. $$What is the corresponding temperature in Fahrenheit?

Accepted Answer

$$T_F = \frac{9}{5}(-2) + 32 = 28.4\ ^\circ\mathrm{F}$$

Question 5

Which of the following best describes the Zeroth Law of Thermodynamics?

Accepted Answer

If object A is in thermal equilibrium with object B, and object C is also in thermal equilibrium with object B, then objects A and C will be in thermal equilibrium if brought into thermal contact.

Question 6

A metal rod of length $$L = 2.0\ \mathrm{m} is $$heated from $$20\ ^\circ\mathrm{C} to$$ $$80\ ^\circ\mathrm{C}. If $$the coefficient of linear expansion is $$\alpha = 1.2 	imes 10$$^{-5}$$\ \mathrm{K}^{-1}$$, what is the change in length?

Accepted Answer

$$\Delta L = \alpha L \Delta T = 1.2 	imes 10$$^{-5}$$ 	imes 2.0 	imes (80 - 20) = 1.44 	imes 10$$^{-3}$$\ \mathrm{m}$$

Question 7

A copper flask ($$\alpha = 17 	imes 10$$^{-6}$$\ \mathrm{K}^{-1}) $$with a volume of $$201\ \mathrm{cm}^3 is $$filled to the brim with olive oil ($$\beta = 0.68 	imes 10$$^{-3}$$\ \mathrm{K}^{-1}). If $$the temperature increases from $$11\ ^\circ\mathrm{C} to$$ $$36\ ^\circ\mathrm{C}$$, how much oil spills from the flask?

Accepted Answer

$$\Delta V = V_0$ (\beta - 3\alpha) \Delta T = 201 	imes (0.68 	imes 10$$^{-3}$$ - 3 	imes 17 	imes 10$$^{-6}$$) 	imes 25 = 3.06\ \mathrm{cm}^3$$

Question 8

When a washer with a hole in the center is heated, what happens to the size of the hole and why?

Accepted Answer

The hole expands along with everything else, every dimension of the washer expands.

Question 9

Which of the following best explains why ice floats on water?

Accepted Answer

Solid water (ice) is less dense than liquid water.

Question 10

A bimetallic strip is made of two metals with different coefficients of linear expansion. When heated, what happens to the strip?

Accepted Answer

The strip bends toward the metal with the lower coefficient of linear expansion.

Question 11

Which of the following is the correct equation for linear thermal expansion?

Accepted Answer

$$\Delta L = \alpha L \Delta T$$

Question 12

If the temperature of a gas is decreased to absolute zero, what happens to the pressure of the gas according to the graph of pressure vs. temperature?

Accepted Answer

The pressure of the gas becomes zero.

Question 13

Which of the following statements about thermal equilibrium is correct?

Accepted Answer

Two objects in thermal contact are in thermal equilibrium when they have equal temperatures and no heat flows between them.

Question 14

Which temperature scale has its zero point at the temperature where all molecular motion ceases?

Accepted Answer

Kelvin

Question 15

A bridge is constructed with expansion joints to account for thermal expansion. If the length of the bridge is $$100\ \mathrm{m}$$ and the temperature can vary by $$40\ ^\circ\mathrm{C}$$, with a coefficient of linear expansion $$\alpha = 1.2 	imes 10$$^{-5}$$\ \mathrm{K}^{-1}$$, what is the maximum change in length?

Accepted Answer

$$\Delta L = \alpha L \Delta T = 1.2 	imes 10$$^{-5}$$ 	imes 100 	imes 40 = 0.048\ \mathrm{m}$$

Question 16

Which of the following best describes the behavior of water between $$0\ ^\circ\mathrm{C}$$ and $$4\ ^\circ\mathrm{C}$$?

Accepted Answer

Water contracts (shrinks) as it is heated from $$0\ ^\circ\mathrm{C} to$$ $$4\ ^\circ\mathrm{C}.$$

Question 17

A hot air balloon rises because the air inside the balloon is heated. Which physical principle explains this phenomenon?

Accepted Answer

The heated air expands, becomes less dense than the cooler air outside, and thus rises.

Temperature and Heat: Foundations of Thermodynamics

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