Using v_rms = sqrt(3RT/M), we solve for T: T = (v_rms^2 * M) / (3R) = (1000^2 * 0.044) / (3 * 8.314) = 700 K.

Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T. Setting v_rms = 300 m/s and M = 28 g/mol, we find T = (M * v_rms^2)/(3R) = 600 K.

Using v_rms = sqrt(3RT/M), rearranging gives T = (v_rms^2 * M) / (3R). Substituting values gives T = 500 K.

Using v_rms = sqrt(3RT/M), we can rearrange to find T = (v_rms^2 * M) / (3R). Plugging in values gives T = (600^2 * 0.02) / (3 * 8.314) = 900 K.

The moment of inertia of a hollow sphere about an axis through its center is I = 2/5 MR^2.

Using v_rms = sqrt(3RT/M), we find v_rms = sqrt(3 * 8.314 * 300 / 0.028) = 600 m/s.

5 kilometers is equal to 5000 meters.

The moment of inertia of a solid sphere about an axis through its center is I = 2/5 MR^2.

During a phase change, the temperature of a substance remains constant while the substance absorbs or releases heat.

In an isochoric process, the volume of the gas remains constant.

In an isochoric process, the volume of the system remains constant.

In an isothermal process for an ideal gas, the internal energy remains constant because the temperature does not change.

The electric field due to a charged plane sheet is directly proportional to the surface charge density. Therefore, if σ is doubled, E also doubles.

The electric field inside a uniformly charged sphere is zero.

The electric field inside a charged conductor in electrostatic equilibrium is zero.

The magnetic field at the center of a circular loop of radius R carrying current I is given by B = μ₀I/(2πR).

According to Ampere's Law, the line integral of the magnetic field around a closed loop equals μ₀ times the total current enclosed by the loop.

According to Gauss's law, the total electric flux through a closed surface is proportional to the total charge enclosed.

The total electric flux through a closed surface is given by Φ = ΣQ_enc/ε₀, where Q_enc is the total charge enclosed.

The total moment of inertia of a composite body about the same axis is the sum of the individual moments of inertia.

The total moment of inertia of a composite body is the sum of the individual moments of inertia: I_total = I1 + I2.

The magnetic field at the center of a loop is inversely proportional to the radius. If the radius is halved, the magnetic field quadruples.

Using Ampere's Law, B = μ₀I/2πR for points outside the cylindrical conductor.

For points outside the cylinder, B = μ₀I/2πr.

The damped frequency is less than the natural frequency due to the effect of damping.

Using the grating equation d sin θ = nλ, where d = 1/500000 m, n = 1, and λ = 600 x 10^-9 m, we find θ ≈ 30 degrees.

If the slit width is halved, the width of the central maximum increases because the angle for the first minimum increases.

The central maximum in a single-slit diffraction pattern is wider than all other maxima.

RMS speed is proportional to the square root of temperature, so v_rms at 600 K = 500 * sqrt(600/300) = 707 m/s.

Using v_rms = sqrt(3RT/M), we calculate v_rms = sqrt(3 * 8.314 * 300 / 0.028) which gives approximately 600 m/s.