In a cyclic process, the net work done is equal to the net heat added to the system, as the internal energy returns to its initial state.

In a damped harmonic oscillator, the amplitude decreases over time due to energy loss.

In a Daniell cell, Zinc acts as the anode.

Using the first-order rate equation, k = (ln[A₀] - ln[A]) / t. Here, k = (ln(0.8) - ln(0.2)) / 20 = 0.0347 min⁻¹.

t₁/₂ = 0.693 / k = 0.693 / 0.03 = 23.1 min.

The cathode reaction must be a reduction reaction, and Cu²⁺ + 2e⁻ → Cu is a common cathode reaction.

The cathode reaction is O₂ + 4e⁻ + 4H⁺ → 2H₂O.

The cathode reaction must be a reduction; Ag⁺ + e⁻ → Ag is the anode reaction.

The cathode reaction is Cu²⁺ + 2e⁻ → Cu.

Number of non-smokers = 50 - 20 = 30. Probability = 30/50 = 3/5.

Efficiency (η) = Work done / Input heat = 300 J / 500 J = 0.6 or 60%.

Probability = Number of winning tickets / Total tickets = 2/10 = 1/5.

Probability = Number of winning tickets / Total tickets = 3/10.

Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, thus R_eq = 2Ω.

Y = 1/R + j(ωC - 1/ωL); calculate Y for given values.

Quality factor Q = (1/R) * √(L/C) = (1/50) * √(0.2/50e-6) = 2.

In a purely capacitive circuit, the current leads the voltage by 90°.

In a purely capacitive circuit, the current leads the voltage by 90 degrees.

Average rate = Δ[A]/Δt = (0.8 - 0.4) / 20 = 0.02 M/min.

For a first-order reaction, if [A] is halved, the rate also halves.

If the rate decreases to one-fourth when concentration is halved, the reaction is second-order.

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

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

According to Le Chatelier's principle, increasing the concentration of reactants will shift the equilibrium position to the right to favor the formation of products.

For a second-order reaction, t₁/₂ = 1 / (k[A₀]) = 1 / (0.05 * 0.1) = 200 s.

f0 = 1 / (2π√(LC)) = 1 / (2π√(0.1 × 100 × 10^-6)) = 159.15 Hz.

Resonant frequency f₀ = 1 / (2π√(LC)) = 1 / (2π√(0.1 * 100e-6)) = 159.15 Hz.

Resonant frequency f = 1/(2π√(LC)) = 1/(2π√(0.1 * 100e-6)) = 159.15 Hz.

For a zero-order reaction, the rate is constant and does not depend on the concentration of reactants. The unit of the rate constant (k) is mol/L·s.

In a zero-order reaction, the rate is constant and does not depend on the concentration of the reactants.