Q: Which of the following best defines one mole of a substance?

The amount of substance that contains exactly $$6.02214076 \times 10$$^{23}$$ elementary entities.

Question 1

Which of the following best defines one mole of a substance?

Accepted Answer

The amount of substance that contains exactly $$6.02214076 	imes 10$$^{23}$$ elementary entities.

Question 2

The equation of state for an ideal gas is given by $$pV = nRT. $$Which of the following statements is correct regarding this equation?

Accepted Answer

It relates the pressure, volume, temperature, and number of moles of a gas in thermodynamic equilibrium.

Question 3

A sample of gas at 1 atm and 273 K occupies a volume of 22.4 L. If the temperature is doubled at constant pressure, what will the new volume be?

Accepted Answer

$$44.8\ \mathrm{L}$$

Question 4

Which of the following expressions correctly gives the mass density $$\rho of an $$ideal gas in terms of its pressure $$p$$, molar mass $$M$$, and temperature $$T$$?

Accepted Answer

$$\rho = \dfrac{pM}{RT}$$

Question 5

According to kinetic theory, what is the average translational kinetic energy per molecule of an ideal gas?

Accepted Answer

$$K_{\mathrm{av}} = \dfrac{3}{2}kT$$

Question 6

A piston compresses a gas at constant pressure. Which equation gives the work done by the gas during this process?

Accepted Answer

$$W = p \Delta V$$

Question 7

A gas is compressed at a constant pressure of $$0.800$$ atm from $$9.00 L to$$ $$2.00 L. In $$the process, $$400 J of $$energy leaves the gas by heat. What is the change in the internal energy of the gas? ($$1\ \mathrm{atm} = 101325\ \mathrm{Pa})$$

Accepted Answer

$$+167\ \mathrm{J}$$

Question 8

For an isothermal process involving an ideal gas, which of the following is true?

Accepted Answer

$$\Delta U = 0$$ and $$Q = W$$

Question 9

What is the molar heat capacity at constant volume $$C_V$$ for a monatomic ideal gas?

Accepted Answer

$$C_V = \dfrac{3}{2}R$$

Question 10

A 3.50 mol sample of a diatomic ideal gas is heated at constant pressure from 200 K to 350 K. How much heat is added to the gas? ($$C_P = \dfrac{7}{2}R)$$

Accepted Answer

$$15.3\ \mathrm{kJ}$$

Question 11

Which of the following best describes an adiabatic process?

Accepted Answer

No heat is exchanged with the surroundings ($$Q = 0).$$

Question 12

For an ideal gas, what is the relationship between the molar heat capacities at constant pressure $$C_P$$ and constant volume $$C_V$$?

Accepted Answer

$$C_P = C_V + R$$

Question 13

Which of the following is the correct expression for the root-mean-square (rms) speed of a gas molecule?

Accepted Answer

$$v_{\mathrm{rms}} = \sqrt{\dfrac{3kT}{m}}$$

Question 14

A gas undergoes an isochoric process. Which of the following statements is true?

Accepted Answer

The volume remains constant and $$W = 0.$$

Question 15

For an adiabatic process in an ideal gas, the adiabatic exponent $$\gamma is $$defined as $$\gamma = \dfrac{C_P}{C_V}. $$What is $$\gamma$$ for a monatomic ideal gas?

Accepted Answer

$$\dfrac{5}{3}$$

Question 16

Which of the following statements about the Maxwell-Boltzmann distribution is correct?

Accepted Answer

It describes the distribution of molecular speeds in a gas at a given temperature.

Question 17

If a system absorbs 500 J of heat and does 200 J of work on the surroundings, what is the change in its internal energy?

Accepted Answer

$$\Delta U = 300\ \mathrm{J}$$

Question 18

Which of the following is NOT an assumption of the kinetic theory of gases?

Accepted Answer

Gas molecules interact via long-range attractive forces.

Question 19

During an isothermal expansion of an ideal gas from $$V_1 to$$ $$V_2$$, the work done by the gas is given by:

Accepted Answer

$$W = nRT \ln \left( \dfrac{V_2$}{V_1$} \right)$$

Chapter 15: Thermal Properties of Matter – Study Notes

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