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 sec Godzilla cat, 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 m dash height about 7.5 times the height of the head, and mouth about 1/4 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 breath17 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 m 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 powder? 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

This hypothetical question could be answered like this. One has to be careful of units!!

The energy equation : CpT + 1/2 ( V^2) + p/rho = constant

Cp = 1000 J/kq deg,

rho = density of air at the the mouth of Godzilla, ( temp 1800K)

Using perfect gas aprox, density = P/(RT) where P = atmos pressure ( 103 Kpa), R = 287 J/Kg Deg

density becomes approx .00022 Kg/m^3

Also Cp for air approx 1 Kj/kg ( assumed constant)

Now if the velocity is sonic speed, the stagnation temp is T0/T = 1 + (1.4-1)/2 M^2) M=1, so stagnation temp

is 1.2 times the ambient

Now the enrgy eqn can be set up equating to the RHS Cp *1.2* Ambient temp = Cp*1.2*1800 =2160 J/Kg

In fact this is enough to solve the problem. If one knows the volume of air exhaled per second from the creatures mouth, the energy contained is found from the (mass/second )*2160

The area of the mouth opening is pi*d*d/4 = pi*1.7*1.7/4 = 2.27 m^2

The velocity of air exhaled is sonic = sqrt(1.4 R T) = sqrt ( 1.4 * 287 * 1800) = 850 m/sec

Mass of air exhaled /second = 850 *2.27 m^3/s * density = 850*2.27*.00022 Kg/s = 0.424 Kg/s ( one pound/sec only)

Thus the energy contained in the breath/sec = 2120*( mass/sec) = 900 Joules approx ( 0.9 KJ/sec)

I joule = .239 calories, so 215 cal/sec is lost in the breath per second

If Godzilla eats one BIGMAC, with 2.6 MJ, this should sustain Godzilla for 2890 seconds or 48 minutes.!!!

The entropy change is obtained by dividing the enthalpy change by the temp, for infinite surroundings

Entropy change approx 900/1800 J/deg/s or 0.5 J/deg/sec

Now one Watt* 1 second = 1 Joule

900 Joules = 900watt in one second

The power in the electric line is 1.32KW, in one second this is 1.32KJ which is larger than 900 J (on one secomd)

But if Godzilla exhales for 5 seconds , the recharge wont last.