Final answer:
The option that represents the first law of thermodynamics is 'Energy lost by the system must be gained by the surroundings.' It reflects the principle of conservation of energy in a closed system, where energy can be transferred or transformed but not created or destroyed.
Step-by-step explanation:
The statement of the first law of thermodynamics among the given options is 'd. Energy lost by the system must be gained by the surroundings.' This version of the first law, also known as the law of conservation of energy, implies that the total amount of energy in a closed system remains constant; energy can neither be created nor destroyed. It can only change forms or be transferred from one object to another. A more formal mathematical statement is ΔU = Q - W, where ΔU represents the change in internal energy, Q is the net heat transferred into the system, and W is the net work done by the system.
Using an example mentioned in the provided materials, if you put 12.0 gallons of gasoline into a car's tank, and the energy content of the gasoline is 1.3 × 108 J/gal, you can calculate the change in internal energy of the car. Assuming all other factors like the car's temperature remain constant, the total internal energy change (ΔU) of the car is the energy content of the fuel added, which can be calculated by multiplying the quantity of gasoline in gallons by the energy content per gallon. Hence, the change in internal energy would be 12.0 gal × 1.3 × 108 J/gal = 1.56 × 109 J.