Final answer:
The heat transferred from the sprinter's body to the surroundings during the event is -2.7 x 10^5 J, as calculated using the first law of thermodynamics.
Step-by-step explanation:
The question is about the calculation of heat transfer in a physical process, using the first law of thermodynamics. The first law of thermodynamics relates the change in internal energy (\( \Delta U \)) of a system to the heat transfer (\( Q \)) to and from the system and the work (\( W \)) done by or on the system. It is given by the equation:
\[ \Delta U = Q - W \]
For the sprinter, we know the work done (\( W = 4.8 \times 10^5 \, \text{J} \)) and the change in internal energy (\( \Delta U = -7.5 \times 10^5 \, \text{J} \)). The negative sign indicates a decrease in internal energy. To find the heat transfer, we rearrange the first law of thermodynamics as follows:
\[ Q = \Delta U + W \]
Substituting the given values:
\[ Q = (-7.5 \times 10^5 \, \text{J}) + (4.8 \times 10^5 \, \text{J}) \]
\[ Q = -2.7 \times 10^5 \, \text{J} \]
The negative sign of \( Q \) indicates that heat is transferred from the sprinter's body to the surroundings. Therefore, during the event, the heat transferred from the sprinter's body to the surroundings is \( -2.7 \times 10^5 \, \text{J} \).