The moment of inertia is smallest when all mass is concentrated at the center, as it minimizes the distance from the axis of rotation.

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

Both expressions are valid for calculating the RMS speed of a monoatomic ideal gas.

The electric field due to a point charge varies as E = kQ/r², where k is a constant.

A reversible process must be quasi-static, meaning it occurs infinitely slowly.

ΔG = ΔH - TΔS = 200 kJ - 400 K * 0.5 kJ/K = 200 kJ - 200 kJ = 0 kJ.

The rate of disappearance of A is equal to the rate of formation of B, multiplied by the stoichiometric coefficients. Here, it is 1.0 mol/L/s.

If doubling the concentration of A doubles the rate, the reaction is first order with respect to A.

The correct relationship at constant temperature and pressure is ΔG = ΔH - TΔS.

According to Le Chatelier's principle, if the concentration of products increases, the equilibrium will shift to the left.

At equilibrium, the change in Gibbs free energy (ΔG) is zero, indicating that the system is at maximum entropy.

If ΔG° is negative, the equilibrium constant K is greater than 1.

A positive ΔG° indicates that the reaction is non-spontaneous in the forward direction, thus spontaneous in the reverse.

A positive ΔG° indicates that the reaction is non-spontaneous in the forward direction under standard conditions.

A positive ΔG° indicates that the reaction is non-spontaneous in the forward direction.

For a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant, given by Rate = k[A].

To find the temperature at which the reaction becomes spontaneous, set ΔG = 0: 0 = ΔH - TΔS. Thus, T = ΔH/ΔS = (100,000 J)/(200 J/K) = 500 K.

To find the temperature at which the reaction becomes spontaneous, set ΔG = 0: 0 = ΔH - TΔS, thus T = ΔH/ΔS = 100,000 J / 200 J/K = 500 K.

To find the temperature at which the reaction becomes spontaneous, set ΔG = 0: 0 = ΔH - TΔS, thus T = ΔH/ΔS = (50,000 J/mol) / (100 J/mol·K) = 500 K.

The moment of inertia of a rectangular plate about an axis through its center parallel to side a is I = 1/12 Mb^2.

For a reversible process, the change in entropy is given by ΔS = Q/T, where Q is the heat exchanged and T is the temperature.

The change in entropy (ΔS) for a reversible process is given by ΔS = Q/T, where Q is the heat absorbed and T is the temperature.

For a reversible process, the change in entropy (ΔS) is given by ΔS = Q/T, where Q is the heat absorbed and T is the temperature.

For a reversible process, the change in entropy of the universe is zero, as the system and surroundings are in equilibrium.

The efficiency of a Carnot engine is given by η = 1 - (T2/T1), where T1 is the temperature of the hot reservoir and T2 is the temperature of the cold reservoir.

For a satellite in a circular orbit, the kinetic energy is less than the potential energy, as K.E. = -1/2 P.E.

Low Earth orbit satellites typically operate at altitudes ranging from about 200 km to 2000 km above the Earth's surface.

For a satellite in a stable orbit, the centripetal force required for circular motion equals the gravitational force acting on the satellite.

The angular position of the first minimum is given by sin θ = λ/a.

The magnetic field inside a solenoid is given by B = μ₀nI.