Heat and Thermodynamics

Sample questions

Showing 20 of 70 questions from this chapter. The full bank is in the chapter test below.

1. 1

   Thermodynamics is mainly concerned with

   • A.✓ the conversion of heat into other forms of energy (correct answer)
   • B.the measurement of the quantity of heat
   • C.the transfer of heat from one body to another
   • D.the change of state of a substance

   Why: Thermodynamics deals with the relationships and conversions between heat and other forms of energy. Measuring heat alone, moving heat from place to place, or a change of state is only one part of that wider subject.
2. 2

   Which of the following is an assumption of the kinetic theory of gases?

   • A.The molecules of a gas attract one another with a strong force.
   • B.✓ The volume of the molecules is negligible compared with the volume of the gas. (correct answer)
   • C.The collisions between the molecules are inelastic.
   • D.The molecules move in curved paths between collisions.

   Why: The theory treats the molecules as point masses, so their own volume is negligible beside the volume of the container. It also assumes no intermolecular forces and straight-line motion between collisions.
3. 3

   Collisions of gas molecules with one another and with the walls of the container are perfectly elastic. This means that

   • A.the molecules lose kinetic energy in each collision
   • B.the molecules come to rest after striking the walls
   • C.✓ the total kinetic energy of the molecules is conserved (correct answer)
   • D.the molecules stick together after colliding

   Why: In a perfectly elastic collision there is no net loss of kinetic energy, so the total kinetic energy of the gas molecules stays the same. The molecules do not slow down permanently or stick to the walls.
4. 4

   The pressure exerted by a gas on the walls of its container is due to

   • A.the repulsive forces between the gas molecules
   • B.the weight of the gas molecules
   • C.the attraction between the gas molecules and the walls
   • D.✓ the collisions of the gas molecules with the walls (correct answer)

   Why: The molecules strike the walls a very large number of times each second, and the change of momentum at each impact produces a force on the wall; force per unit area is the pressure. Intermolecular forces and molecular weight do not by themselves create pressure on the walls.
5. 5

   Under which conditions does a real gas behave most nearly like an ideal gas?

   • A.✓ Low pressure and high temperature (correct answer)
   • B.High pressure and low temperature
   • C.Low pressure and low temperature
   • D.High pressure and high temperature

   Why: At low pressure and high temperature the molecules are far apart and move fast, so intermolecular forces and the finite size of the molecules become negligible. At high pressure and low temperature the molecules are crowded together and a real gas deviates greatly from ideal behaviour.
6. 6

   The average kinetic energy of the molecules of a gas is directly proportional to

   • A.the square root of its absolute temperature
   • B.✓ its absolute temperature (correct answer)
   • C.its pressure
   • D.the volume occupied by the gas

   Why: The average kinetic energy of a molecule is $\frac{3}{2}k_BT$, which is directly proportional to the absolute temperature. The mean speed is proportional to the square root of $T$, not the kinetic energy.
7. 7

   Two bodies at different temperatures are placed in thermal contact, and after some time the net flow of heat between them stops. The bodies are now in

   • A.mechanical equilibrium
   • B.chemical equilibrium
   • C.✓ thermal equilibrium (correct answer)
   • D.physical equilibrium

   Why: Bodies at the same temperature are in thermal equilibrium, so there is no temperature difference left to drive a net transfer of heat between them. Mechanical and chemical equilibrium are quite different ideas.
8. 8

   The internal energy of a substance is

   • A.the total heat supplied to it
   • B.the total work done by it
   • C.the average kinetic energy of one of its molecules
   • D.✓ the sum of all forms of molecular kinetic and potential energy in it (correct answer)

   Why: Internal energy is the sum of all the molecular kinetic and potential energies of the substance. It is a function of state, so only its change between two states matters; heat and work are transfers of energy, not energy stored in the body.
9. 9

   For an ideal gas, the internal energy consists of

   • A.✓ the translational kinetic energy of its molecules (correct answer)
   • B.the potential energy of the intermolecular forces
   • C.the vibrational energy of the molecules
   • D.the energy stored in the walls of the container

   Why: An ideal gas has no intermolecular forces, so there is no molecular potential energy and the internal energy is just the translational kinetic energy of the molecules, which depends only on temperature. Rotational and vibrational energies belong to real polyatomic molecules, not to a monatomic ideal gas.
10. 10

    When the temperature of a body rises, its internal energy

    • A.decreases
    • B.✓ increases (correct answer)
    • C.remains the same
    • D.becomes zero

    Why: A rise in temperature means the average kinetic energy of the particles has increased, and this shows up as an increase in the internal energy of the body.
11. 11

    The Boltzmann constant $k_B$ is given by

    • A.$R \times N_A$
    • B.$\frac{N_A}{R}$
    • C.✓ $\frac{R}{N_A}$ (correct answer)
    • D.$R T$

    Why: Comparing $PV = nRT$ with $PV = Nk_BT$ and using $n = N/N_A$ gives $k_B = R/N_A$, the gas constant per molecule rather than per mole.
12. 12

    The value of the Boltzmann constant is

    • A.$6.02 \times 10^{23}\ \mathrm{J\,K^{-1}}$
    • B.$8.31 \times 10^{3}\ \mathrm{J\,K^{-1}}$
    • C.$1.38 \times 10^{-23}\ \mathrm{J\,mol^{-1}\,K^{-1}}$
    • D.✓ $1.38 \times 10^{-23}\ \mathrm{J\,K^{-1}}$ (correct answer)

    Why: $k_B = R/N_A = (8.31\ \mathrm{J\,mol^{-1}\,K^{-1}})/(6.02 \times 10^{23}\ \mathrm{mol^{-1}}) = 1.38 \times 10^{-23}\ \mathrm{J\,K^{-1}}$. The same value quoted per mole rather than per molecule is a unit slip.
13. 13

    If a gas contains $N$ molecules, the number of moles $n$ of the gas is

    • A.✓ $\frac{N}{N_A}$ (correct answer)
    • B.$N \times N_A$
    • C.$\frac{N_A}{N}$
    • D.$N + N_A$

    Why: Avogadro's number $N_A = 6.02 \times 10^{23}$ is the number of molecules in one mole, so the number of moles is the number of molecules divided by $N_A$.
14. 14

    The ideal gas equation expressed in terms of the number of molecules $N$ is

    • A.$PV = NRT$
    • B.✓ $PV = Nk_BT$ (correct answer)
    • C.$PV = \frac{Nk_BT}{R}$
    • D.$PV = \frac{NR}{k_BT}$

    Why: Putting $n = N/N_A$ and $R = N_Ak_B$ into $PV = nRT$ gives $PV = Nk_BT$; here $k_B$ is the Boltzmann constant and $N$ is the number of molecules, not the number of moles.
15. 15

    Two moles of an ideal gas occupy $0.050\ \mathrm{m^3}$ at $300\ \mathrm{K}$. Its pressure is about

    • A.$1.0 \times 10^{4}\ \mathrm{Pa}$
    • B.$2.5 \times 10^{3}\ \mathrm{Pa}$
    • C.✓ $1.0 \times 10^{5}\ \mathrm{Pa}$ (correct answer)
    • D.$5.0 \times 10^{5}\ \mathrm{Pa}$

    Why: $P = \frac{nRT}{V} = \frac{2 \times 8.31 \times 300}{0.050} = 9.97 \times 10^{4}\ \mathrm{Pa}$, which is about $1.0 \times 10^{5}\ \mathrm{Pa}$, close to one atmosphere.
16. 16

    The density $\rho$ of an ideal gas of molar mass $M$ at pressure $P$ and absolute temperature $T$ is

    • A.$\rho = \frac{RT}{PM}$
    • B.$\rho = \frac{MRT}{P}$
    • C.$\rho = \frac{P}{MRT}$
    • D.✓ $\rho = \frac{PM}{RT}$ (correct answer)

    Why: Since $n = m/M$ and $\rho = m/V$, the ideal gas equation rearranges to $\rho = PM/RT$. So the density of a gas is low at low pressure and high temperature, which is exactly when the gas behaves ideally.
17. 17

    Boyle's law states that for a fixed mass of gas at constant temperature

    • A.✓ the product $PV$ is constant (correct answer)
    • B.the ratio $P/V$ is constant
    • C.the sum $P + V$ is constant
    • D.the product $P^2V$ is constant

    Why: At constant temperature $P$ is inversely proportional to $V$, so the product $PV$ stays constant and $P_1V_1 = P_2V_2$. A constant ratio or a constant sum would make the graph a straight line, which it is not.
18. 18

    A gas occupies $6.0\ \mathrm{L}$ at a pressure of $12\ \mathrm{atm}$. If the pressure is increased by $2.0\ \mathrm{atm}$ at constant temperature, the new volume is

    • A.$4.0\ \mathrm{L}$
    • B.✓ $5.1\ \mathrm{L}$ (correct answer)
    • C.$7.0\ \mathrm{L}$
    • D.$3.4\ \mathrm{L}$

    Why: The final pressure is $12 + 2.0 = 14\ \mathrm{atm}$, and $P_1V_1 = P_2V_2$ gives $V_2 = (12)(6.0)/14 = 5.1\ \mathrm{L}$. An increasing pressure must give a smaller volume, so answers larger than $6.0\ \mathrm{L}$ are impossible.
19. 19

    The graph of pressure against volume for a fixed mass of gas at constant temperature is

    • A.a straight line through the origin
    • B.a straight line with a negative slope
    • C.✓ a curve called an isotherm (correct answer)
    • D.a horizontal straight line

    Why: At constant temperature $P$ is inversely proportional to $V$, so the graph is a hyperbola called an isotherm. A straight line through the origin is the volume-temperature graph of Charles' law, not a pressure-volume graph.
20. 20

    Charles' law states that at constant pressure the volume of a fixed mass of gas is

    • A.inversely proportional to its absolute temperature
    • B.independent of its temperature
    • C.proportional to the square of its absolute temperature
    • D.✓ directly proportional to its absolute temperature (correct answer)

    Why: At constant pressure $V \propto T$, with $T$ measured in kelvin, so $V/T$ is constant. On a volume against temperature graph this is a straight line through the origin.