The particulate nature of matter practice questions.

In the kinetic theory of gases, the absolute temperature of an ideal gas is proportional to the average...

• speed of the molecules
• kinetic energy of the molecules
• potential energy of the molecules
• size of the molecules

Answer: kinetic energy of the molecules

Average translational KE = (3/2)kT, so temperature (in kelvin) is proportional to the average kinetic energy of the molecules.

Which statement correctly distinguishes an isothermal from an adiabatic process for an ideal gas?

• Isothermal: ΔU = 0 (Q = W); Adiabatic: Q = 0 (ΔU = −W)
• Isothermal: Q = 0; Adiabatic: ΔU = 0
• Both of these processes always have exactly Q = 0 throughout the whole change
• Both have ΔU = 0

Answer: Isothermal: ΔU = 0 (Q = W); Adiabatic: Q = 0 (ΔU = −W)

Using Q = ΔU + W, where W is the work done by the gas: isothermal keeps T constant, so ΔU = 0 and Q = W; adiabatic exchanges no heat (Q = 0), so ΔU = −W. Swapping the two conditions gives the most tempting wrong option.

A fixed mass of ideal gas is held at constant volume while its absolute (kelvin) temperature is doubled. Its pressure will

• halve
• stay the same
• double
• quadruple

Answer: double

At constant volume p ∝ T (Gay-Lussac's law), so doubling the kelvin temperature doubles the pressure.

Two 6.0 Ω resistors are connected in parallel. Their combined resistance is

• 3.0 Ω
• 6.0 Ω
• 12 Ω
• 0.33 Ω

Answer: 3.0 Ω

1/R = 1/6.0 + 1/6.0 = 2/6.0, so R = 3.0 Ω. Two equal resistors in parallel give half the value of one.

The radiation emitted by a black body has maximum intensity at a wavelength of 580 nm. Using Wien's displacement law (constant = 2.9 × 10⁻³ m K), the surface temperature of the body is approximately:

• 500 K
• 2900 K
• 50 000 K
• 5000 K

Answer: 5000 K

T = 2.9 × 10⁻³ / (580 × 10⁻⁹) = 5000 K. Power-of-ten slips give 500 K or 50 000 K; hotter bodies peak at shorter wavelengths.

The absolute temperature of a black body is doubled while its surface area stays constant. The total power it radiates increases by a factor of:

• 2
• 4
• 8
• 16

Answer: 16

The Stefan–Boltzmann law gives P = σAT⁴, so doubling T multiplies the power by 2⁴ = 16. Choosing 2 or 4 comes from forgetting the fourth-power dependence.