KEY2CHEM

Energy Conservation during Energy Transfer

When two objects with different internal energies (through some combination of heat and work) are put into contact with one another, one object will transfer energy to the other object until the two reach equilibrium. In the case of thermal equilibrium, the two objects will come to the same final temperature. The energy lost by one object will be equal in magnitude to the energy gained by the other object. For example, $$\Delta E_{system} = -\Delta E_{surroundings}$$. The energy is transferred but its magnitude is conserved.

Example 1.

A piston does $$15\text{ J}$$ of work on its surroundings. What is the change in energy of the surroundings?

A. $$+15\text{ J}$$

B. $$-15\text{ J}$$

C. $$0\text{ J}$$

Solution

A. $$+15\text{ J}$$

In this case, energy is being transferred as work. Work going out of the system (the piston) is negative.

$$\Delta E_{system} + \Delta E _{surroundings} = 0$$

$$\Delta E_{surroundings} = -\Delta E_{system} = -(-15 \text{ J}) = + 15 \text{ J}$$

Example 2.

The internal energy lost by a system is _______ by the surroundings.

A. lost

B. gained

C. destroyed

Solution

B. gained

Energy is conserved, meaning energy lost by a system is gained by the surroundings.

Example 3.

A system gains $$3\text{ kJ}$$ of energy from its surroundings. Which statement is true?

A. The energy of the system decreases by $$3\text{ kJ}$$.

B. The energy of the surroundings increases by $$3\text{ kJ}$$.

C. The energy of the surroundings decreases by $$3\text{ kJ}$$

Solution

C. The energy of the surroundings decreases by $$3\text{ kJ}$$.

The energy transferred out of the surroundings goes into the system.