Godzilla wreaks an awful lot of destruction in its movies wi

Godzilla wreaks an awful lot of destruction in its movies, with its “atomic breath” being able to melt tanks and electricity transmission towers, as well as cause airplanes and buildings to explode. But we never see Godzilla eat, so the question is “Can Godzilla can store enough energy for a Tokyo rampage before its next meal? Some pertinent data follow.

Godzilla’s height has varied from 50 m (original 1954 movie) to many times that (2014 version). We’ll go with the classical value.

We’ll estimate the size of Godzilla’s mouth by taking proportions to be the same as that for an average human—height about 7.5 times the height of the head, and mouth about 14 of the head height. That means Godzilla’s mouth is about 1.7 m in diameter.

How about the temperature of Godzilla’s “atomic breath.” It will melt a tank with no problem and in 1954 that meant about 1590 K for carbon steel. (Nowadays, with B4C armor it’s >3036 K. Godzilla must be mutating or evolving). Since the original Godzilla movie was in the 1950’s we’ll take a tank melting temperature of 1590 K. Godzilla’s breath temperature must be much higher, let’s agree on 1800 K.

What about the speed of Godzilla’s breath? We’ll choose the sonic speed, which at 1800 K for air is 850 m/s. Why air? Well every creature on earth breathes it in and out so we’ll assume Godzilla does too. We’ll also take the breath air pressure to be 1 bar.

Now answer the following questions:

What is Godzilla’s energy loss rate when he exhales his atomic breath?

Report your answer in kJ, then in kcal. Also report your answer in Big Macs consumed/sec (One Big Mac contains 2.6 MJ!).

What is the corresponding entropy loss rate?

Godzilla is often seen crashing through high voltage electrical lines. Instead of getting his energy from organic material, it might get it from the electrical grid. If the grid voltage is 110 kV and the current 120 A, what is the corresponding electrical power? What is the corresponding rate of entropy change?

If Godzilla’s exhaling time is between 2 and 5 seconds, and its time in contact with the high voltage power lines is 1 second, Can it rebuild its energy stores? What is its net change in entropy due to atomic breath and electrical charging?

Solution

Volume of air flow rate out of the Godzilla = area x velocity = pi/4 x 1.7^2 x 850 = 1929.33 m3/s.

Apply ideal gas equation : PV = mRT

Or, 100 x 1929.33 = m x 0.287 x 1800

Or, m = 373.47 kg/s.

Energy associated with this mass flow rate per second = mcpT = 373.47 x 1.237 x 1800 = 831568.3 kJ

One Big Mac = 2.6 MJ i.e Energy exhales by Godzilla = 831568.3/(1000 x 2.6) = 319.83 Big Macs.

Entropy loss rate = dQ/T =831568.3/1800 = 461.98 kJ/kg-K.

Electrical Power = 110 x 120 = 13200 kW

Exhaling power = 831568.3/5 = 166313.66 kW (Assuming 5 second is the exhaling time)

So, exhaling power is more than the power Godzilla gets from electrical energy. So, it can not build its energy stores by this way.

Net energy change due to atomic breadth and electrical charging = (166313.66 - 13200)/1800 = 85.063 kJ/kg-K.