The freezing point of urine depends on the concentration of urine, which depends on the quantity of salts, urea, and various other organic substances present. With human urine, that depends mainly on fluid intake, and next the diet. Urine from vegetarians is somewhat different to that from carnivores. Other factors will also cause variation in the composition , such as if the source led a sedentary or an active lifestyle. Age and sex also affect the composition of urine, as do metabolic and genetic factors.
The volume of fluid drunk naturally affects the concentration of urine, as does the nature of the fluid – alcohol or coffee, for example.
Finally, the age of the urine will affect the chemical composition. Rancid urine has much more free ammonia, and ammonium salts, and a lot less urea than a fresh sample.
Now, let us assume that the person is normal and drinks good amount of water, so the freezing point will be around -5 degree centigrade. having established this we’ll now look at the temperature at which urine comes out of the body. of course it usually comes out at the body temperature i.e. 37 degree centigrade.
next, let’s assume the height from where the man is pissing to the ground is 0.8m ( a little less than half of average height)
considering a uniform flow and the force with which it comes out is ignored (should not be actually), the time it takes to reach the ground is 0.4 seconds.
( assumed 90 degree w.r.t. ground)
Thus, within the span of 0.4 seconds temperature should be decreased from 37 to -5 degrees i.e. a change of 42 degrees.
now we use Newton’s law of cooling, the equation is- T(T) = Ta + (To – Ta)E-Kt
where, T(t)= -5 degrees
T(a) is the ambient temperature that we have to find out.
T(0) = 37 degrees.
t = 0.4 sec
the catch is we have no information about k, which governs the rate of cooling.
let’s assume it to be- k= 0.02.
we’ll substitute these values in the equation, to obtain the temperature outside
which is lesser than -2000 degree Celsius, which in the world is impossible or theoretically not possible.