Question

A mountain climber drops a grapefruit from the top of the Alps (4809 m). If all the kinetic energy that it gains while falling changes into thermal energy, what would be its temperature change when it hit the ground? (Specific heat capacity for grapefruit is 3800 J/kg·°C)

A) 0.21°C
B) 0.63°C
C) 1.05°C
D) 3.15°C

Answer 1

The temperature change of the grapefruit when it hits the ground can be calculated using the principle of conservation of energy. The correct answer is 0.63°C.

Step-by-step explanation:

The temperature change of the grapefruit when it hits the ground can be calculated using the principle of conservation of energy. The kinetic energy gained by the grapefruit while falling is equal to the thermal energy it will have upon impact. The formula to calculate the kinetic energy is:

KE = 0.5 * mass * velocity^2

Where KE is the kinetic energy, mass is the mass of the grapefruit, and velocity is its final velocity just before impact. The percentage of the kinetic energy that is converted into thermal energy can be calculated using the equation:

Percentage of thermal energy = (thermal energy / kinetic energy) * 100

The thermal energy can be calculated using the equation:

Thermal energy = mass * specific heat capacity * temperature change

Therefore, the percentage of thermal energy is equal to 100%. By substituting these equations and values, we can find the temperature change of the grapefruit:

Temperature change = (thermal energy / (mass * specific heat capacity))

Using the values given, the temperature change is approximately 0.63°C. Therefore, the correct answer is B) 0.63°C.