KEY2CHEM

Energy Conservation

As stated by the First Law of Thermodynamics, energy is neither created or destroyed. Energy can be transferred between system and surroundings; the magnitude of energy is unchanged even as it is transferred. Energy can be transferred as heat ($$q$$) or work ($$w$$), with the total change in internal energy described as $$\Delta E$$ and where $$\Delta E = q + w$$.

Transferring energy from the surroundings into the system increases the energy of the system, so $$\Delta E > 0$$. Transferring energy from the system to the surroundings decreases the energy of the system, so $$\Delta E < 0$$.

Example 1.

When the energy of the system decreases, what is the sign of $$\Delta E _{system}$$?

A. positive

B. zero

C. negative

Solution

C. negative

When the system of the energy decreases, energy is transferred out of the system, so $$\Delta E_{system} < 0$$.

Example 2.

A system gains $$25\text{ J}$$ of heat from its surroundings and does  $$15\text{ J}$$ of work on its surroundings. What is $$\Delta E$$ of the system?

A. $$-40\text{ J}$$

B. $$10\text{ J}$$

C. $$-10\text{ J}$$

Solution

B. $$10\text{ J}$$

Energy transfer into the system is positive, and energy transfer out of the system is negative. $$\Delta E = q + w = 25 \text{ J} + (-15 \text{ J}) = 10 \text{ J}$$

Example 3.

Which would result in an increase in energy of the system?

A. The surroundings absorb $$5\text{ J}$$ of heat from the system.

B. The surroundings do $$8\text{ J}$$ of work on the system.

C. The system does $$3\text{ J}$$ of work on the surroundings.

Solution

B. The surroundings do $$8\text{ J}$$ of work on the system.

When the surroundings do work on the system, the system of the energy is increased ($$\Delta E > 0$$).