Final answer:
The energy dissipated by a lightning bolt with given parameters is 2.00 × 10¹ joules, which can cause substantial damage by heating and vaporizing materials such as tree sap. Lightning is most likely to occur during the mature stage of a thunderstorm and can happen across various temperature ranges.
Step-by-step explanation:
The energy dissipated by a lightning bolt can be calculated using the formula for electrical power: energy (E) equals current (I) times voltage (V) times time (t). For a lightning bolt with a current of 20,000 A, a voltage of 1.00 × 10² MV, and a duration of 1.00 ms, the energy E is given by:
E = I × V × t
E = 20,000 A × 1.00 × 10¸ V × 1.00 × 10⁻³ s
E = 2.00 × 10¹ joules (J)
This energy is sufficient to heat and vaporize a substantial quantity of water, causing significant damage if it strikes an object, such as a tree. For example, the heating and vaporization of tree sap with this energy can be estimated by considering the specific heat capacity and heat of vaporization of water, which are approximately 4.18 J/g°C and 2260 J/g, respectively.
A lightning strike typically occurs at the mature stage of a thunderstorm when the atmospheric conditions are ripe for the formation of lightning. The likelihood of lightning increases as the temperature rises because warm air can hold more water vapor, contributing to the conditions necessary for thunderstorm development. However, lightning can occur across a wide range of temperatures whenever the atmospheric conditions are suitable.