Work done (W) = P * ΔV = P * (V2 - V1).

According to Boyle's Law, P1V1 = P2V2, thus P2 = P1(V1/V2).

In an isothermal process, the work done by the gas is equal to the heat absorbed. Therefore, work done = 600 J.

Work done (W) = nRT ln(Vf/Vi). Here, nRT = PVi = 100 kPa * 1 m³ = 100 kJ. W = 100 kJ * ln(2) ≈ 69.3 kJ.

Work done (W) = P * ΔV = 100 kPa * (2 m³ - 1 m³) = 100 kPa * 1 m³ = 100 kJ = 10 kJ.

In an adiabatic compression, the temperature of the gas increases due to work done on it.

Using Boyle's Law, P1V1 = P2V2, we find P2 = P1 * (V1/V2) = 1 atm * (4 L / 1 L) = 4 atm.

Probability of chocolate candy = 4/10 = 2/5.

Total marbles = 4 + 5 + 1 = 10. Probability of yellow = 5/10 = 1/2.

Total marbles = 6 + 4 = 10. Probability of yellow marble = 4/10 = 2/5.

Total marbles = 7 + 5 + 8 = 20. Probability of blue marble = 5/20 = 1/4.

Total marbles = 8 + 4 = 12. Probability of blue marble = 4/12 = 1/3.

Total marbles = 8 + 6 + 4 = 18. Probability of blue marble = 6/18 = 1/3.

According to the law of reflection, the angle of reflection is equal to the angle of incidence. Therefore, the angle of reflection is also 30 degrees.

Using the right-hand rule, the magnetic field direction at a point above the wire is away from the wire.

As the loop enters the magnetic field, the change in magnetic flux increases, leading to an increase in the induced current.

When a loop of wire is placed in a changing magnetic field, electromagnetic induction occurs, generating an electromotive force (EMF) in the loop.

If the magnetic field strength increases, the magnetic flux through the loop increases, inducing a current according to Faraday's law.

According to Faraday's law, an increase in magnetic field through the loop induces a current in the loop, which increases as the rate of change of magnetic flux increases.

As the loop rotates, the angle between the magnetic field and the normal to the loop changes, which causes the direction of the induced current to reverse periodically.

Efficiency = (Output Work / Input Energy) * 100 = (1200 J / 2000 J) * 100 = 60%.

Power (P) = Work (W) / Time (t). P = 1500 J / 30 s = 50 W.

Using the right-hand rule, if the magnetic field is into the paper and the charge moves to the right, the force will be upwards.

Period (T) = 1 / frequency (f) = 1 / 1 Hz = 1 s.

Period (T) = 1 / Frequency (f) = 1 / 2 Hz = 0.5 s.

The period T is the reciprocal of frequency f. Thus, T = 1/f = 1/2 = 0.5 s.

Frequency f = 1/T = 1/2 s = 0.5 Hz.

At the top, T + mg = mv²/L. T = mv²/L - mg.

The frequency f of a mass-spring system is given by f = (1/2π)√(k/m). Here, f = (1/2π)√(200/0.5) ≈ 2 Hz.

Angular frequency ω is related to frequency f by ω = 2πf. Therefore, for f = 1 Hz, ω = 2π(1) = 2π rad/s.