Condensation generates 2.5 time 10^6 J of energy for every kg of water that cond

Question

Condensation generates 2.5 time 10^6 J of energy for every kg of water that condenses. Estimate the amount of potential energy contained in an ordinary thunderstorm. If you could somehow harness this energy, how long could you provide power for the city of State College (~100.000 people)? In class, we discussed that the velocity (v_t) of each gas molecule, i, that compose an air parcel can be broken into a component associated with the random motion (v_r, t) and the overall center of mass motion (v_cm), or v_r = v_r, t + v_cm. Please show that the time-rate-of change of the total kinetic energy of the air parcel can be written as: sigma^N_t=1 1/2 m_i dV_i/dt. v_i = d/dt (sigma^N_t=1 1/2 m_i v_r^2, i + 1/2 M v^2_cm) = d/dt (KE_internal + KE_cm) where M is the total mass of the parcel, and N is the total number of molecules that compose the parcel.

Explanation / Answer

Time elapsed = (B x C)/A

=(2.5 *10^9)*365/1055

= 864928910 days

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