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A blow to the head can cause the retina, the sight-giving lining of one's eye, to tear or detach from the inner surface of the orb, to float in its aqueous. For a minor tear sight might be restored by "welding" the retina back to the wall of the eye with carefully applied blasts of a laser powered at 103W/mm2. Use the information given.
Calculate the correct time, of duration, of applied laser power?
♦ The power a laser delivers is focused and substantial; 103W/mm2. The target is one square millimeter of surface of one cubic millimeter of injured retinal tissue. The tool is to sear the tissue and cause its temperature to attain 98°C - in one firing. The initial temperature of the tissue is 38°C.
The energy equation is applied with the cubic millimeter of retinal tissue as the system. Kinetic and potential energy changes are zero.
Bring the term, "pdV", th the left. Pressure is constant, the term combines with "du" to become "dh." Next apply integrals:
The differential, dh, is called exact; it integrates immediately. We use an average specific heat to represent the enthalpy difference. The laser power is a function of time, W-dotlaser/A(t) and area. It might be that the device has a start-up transient. But our calculation is preliminary so we apply the mean value theorem to effect the integration. Also apply the numbers and properties of water.
The mechanism of the laser is work. The effect is increased temperature. The trauma of being seared causes the tissue to adopt a "heal and repair" physiological mode. The sear does not occur as a consequence of temperature difference, hence is not heat.