Explanation

To find the increase in internal energy, we can use the equation:

ΔU = Q - W

where ΔU is the change in internal energy, Q is the heat energy added (which is the latent heat of vaporization in this case), and W is the work done.

Given:

Q = 2240 J (latent heat of vaporization of water per gram)

W = 168 J (work done in the process of vaporization)

Now, we can plug in the values:

ΔU = Q - W

= 2240 J - 168 J

= 2072 J

Explanation

To calculate the moment of inertia of the Earth about its diameter, we can use the formula for the moment of inertia of a sphere:

I = (2/5)MR^2

where:

I = moment of inertia

M = mass of the Earth (10^25 kg)

R = radius of the Earth (diameter/2 = 12800 km / 2 = 6400 km = 6.4 × 10^6 m)

Plugging in the values, we get:

I = (2/5) × 10^25 kg × (6.4 × 10^6 m)^2

= (2/5) × 10^25 kg × 4.096 × 10^13 m^2

= 1.6384 × 10^38 kg m^2

≈ 1.64 × 10^38 kg m^2

Explanation

To calculate the velocity attained by the rocket, we can use the equation:

F × t = m × Δv

where:

F = force applied (5 × 10^5 N)

t = time (20 s)

m = mass of the rocket (2 × 10^4 kg)

Δv = change in velocity (final velocity - initial velocity)

Since the rocket starts from rest, the initial velocity is 0. Therefore, Δv = final velocity.

Rearranging the equation to solve for Δv, we get:

Δv = F × t / m

= (5 × 10^5 N) × (20 s) / (2 × 10^4 kg)

= 500 m/s