Q: A helium atom has a mass of $$4$$ amu. If the temperature is $$6000\,\text{K}$$, what is the root mean square (rms) speed of the helium atom? (Given: $$1\,\text{amu} = 1.66 \times 10$$^{-27}$$\,\text{kg}$$, $$k_B = 1.38 \times 10$$^{-23}$$\,\text{J/K})$$

$$v_{\text{rms}} = \sqrt{\frac{3k_BT}{m}} = 6.1 \times 10^3$\,\text{m/s}$$

Q: If the mass of a gas particle is doubled, what happens to its root mean square speed ($$v_{\text{rms}}) at $$constant temperature?

$$v_{\text{rms}}$$ decreases by a factor of $$\sqrt{2}$$

Q: The specific heat capacity ($$c) of $$water is $$4.186\,\text{J/g}\cdot\text{C}. $$How much heat is required to raise the temperature of $$18\,\text{kg} of $$water by $$80\,\text{C}$$?

$$Q = mc\Delta T = (18\,\text{kg})(4186\,\text{J/kg}\cdot\text{C})(80\,\text{C}) = 6,028,800\,\text{J}$$

Q: The diffusion constant $$D$$ for a molecule in water is $$1 \times 10$$^{-5}$$\,\text{m}^2/\text{s}. $$What is the average distance $$x_{\text{rms}} a $$molecule diffuses in $$t = 0.115\,\text{s}$$?

$$x_{\text{rms}} = \sqrt{2Dt} = \sqrt{2 \times 1 \times 10$$^{-5}$$ \times 0.115} \approx 1.5 \times 10$$^{-3}$$\,\text{m}$$

Q: Convert $$2500\,\text{Cal} to $$joules. (Given: $$1\,\text{Cal} = 4186\,\text{J})$$

$$2500 \times 4186 = 10,465,000\,\text{J}$$

Question 1

Which equation best describes the relationship between pressure, volume, and temperature for an ideal gas?

Accepted Answer

$$PV = nRT$$

Question 2

A helium atom has a mass of $$4$$ amu. If the temperature is $$6000\,	ext{K}$$, what is the root mean square (rms) speed of the helium atom? (Given: $$1\,	ext{amu} = 1.66 	imes 10$$^{-27}$$\,	ext{kg}$$, $$k_B = 1.38 	imes 10$$^{-23}$$\,	ext{J/K})$$

Accepted Answer

$$v_{	ext{rms}} = \sqrt{\frac{3k_BT}{m}} = 6.1 	imes 10^3$\,	ext{m/s}$$

Question 3

If the mass of a gas particle is doubled, what happens to its root mean square speed ($$v_{	ext{rms}}) at $$constant temperature?

Accepted Answer

$$v_{	ext{rms}}$$ decreases by a factor of $$\sqrt{2}$$

Question 4

Brownian motion is best explained as:

Accepted Answer

Random movement of particles due to collisions with molecules of the surrounding fluid

Question 5

A protein takes $$1$$ second on average to diffuse $$1\,\mu	ext{m} in $$water. How long will it take to diffuse $$3\,\mu	ext{m}$$? (Assume $$x = \sqrt{2Dt})$$

Accepted Answer

$$t = \frac{x^2$}{2D} = 9$$ seconds

Question 6

Which of the following statements about the Kelvin scale is correct?

Accepted Answer

Zero Kelvin corresponds to zero kinetic energy and no molecular motion

Question 7

The specific heat capacity ($$c) of $$water is $$4.186\,	ext{J/g}\cdot	ext{C}. $$How much heat is required to raise the temperature of $$18\,	ext{kg} of $$water by $$80\,	ext{C}$$?

Accepted Answer

$$Q = mc\Delta T = (18\,	ext{kg})(4186\,	ext{J/kg}\cdot	ext{C})(80\,	ext{C}) = 6,028,800\,	ext{J}$$

Question 8

A calorimeter contains $$825\,	ext{g} of $$water at $$12.0\,	ext{C}$$ and $$145\,	ext{g} of $$aluminum at $$12.0\,	ext{C}. If$$ $$265\,	ext{g} of $$copper at $$100.0\,	ext{C} is $$added, what is the equilibrium temperature? (Given: $$c_{	ext{Cu}} = 385\,	ext{J/kg}\cdot	ext{C}$$, $$c_{	ext{Al}} = 900\,	ext{J/kg}\cdot	ext{C}$$, $$c_{	ext{H}_2$$	ext{O}} = 4186\,	ext{J/kg}\cdot	ext{C}$$)

Accepted Answer

$$T_f \approx 18.5\,	ext{C}$$

Question 9

Which of the following best describes the equipartition theorem?

Accepted Answer

Each degree of freedom contributes $$\frac{1}{2}k_BT to $$the average energy

Question 10

If an ideal gas is compressed with no change in temperature, what happens to the speed of its molecules?

Accepted Answer

The speed remains unchanged

Question 11

A membrane is permeable to water but not to solute. What happens when two solutions of different solute concentrations are separated by this membrane?

Accepted Answer

Water passes through the membrane until both sides have equal solute concentrations

Question 12

The diffusion constant $$D$$ for a molecule in water is $$1 	imes 10$$^{-5}$$\,	ext{m}^2/	ext{s}. $$What is the average distance $$x_{	ext{rms}} a $$molecule diffuses in $$t = 0.115\,	ext{s}$$?

Accepted Answer

$$x_{	ext{rms}} = \sqrt{2Dt} = \sqrt{2 	imes 1 	imes 10$$^{-5}$$ 	imes 0.115} \approx 1.5 	imes 10$$^{-3}$$\,	ext{m}$$

Question 13

Convert $$2500\,	ext{Cal} to $$joules. (Given: $$1\,	ext{Cal} = 4186\,	ext{J})$$

Accepted Answer

$$2500 	imes 4186 = 10,465,000\,	ext{J}$$

Question 14

Which of the following is NOT a unit of energy?

Accepted Answer

Degree Celsius ($$	ext{C})$$

Question 15

The flux $$J of $$particles through an area $$A is $$given by $$J = D \frac{\Delta C}{\Delta x}. $$Which factor will increase the flux?

Accepted Answer

Increasing the concentration gradient $$\frac{\Delta C}{\Delta x}$$

Question 16

If the average kinetic energy of a gas molecule is $$\frac{3}{2}k_BT$$, what happens to the kinetic energy if the temperature is doubled?

Accepted Answer

The kinetic energy doubles

Question 17

A gas particle bounces off a wall, causing a change in acceleration. What is the physical quantity associated with this change?

Accepted Answer

Pressure

Question 18

Which of the following best describes the relationship between pressure, volume, and energy for an ideal gas?

Accepted Answer

Pressure times volume has units of energy (Joules)

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