Question

400 kJ of energy is produced by a system at 100 K. What is the change in entropy of the surroundings?
Group of answer choices

+ 4 kJ/K

0 kJ/K. The entropy change is to the system, not the surroundings.

- 4 kJ/K

The change in enthalpy of the surroundings must be known to do the calculation.

Answer 1

To determine the change in entropy of the surroundings when a system produces energy, we can use the formula for the change in entropy:

\[
\Delta S = \frac{Q}{T}
\]

where:
- \( Q \) is the heat exchanged (in this case, energy produced by the system, which is 400 kJ),
- \( T \) is the temperature in Kelvin (in this case, 100 K).

Since the system is producing energy, it is releasing heat to the surroundings, so \( Q \) will be negative for the surroundings:

\[
Q = -400 \text{ kJ}
\]

Now we can calculate the change in entropy of the surroundings:

\[
\Delta S_{\text{surroundings}} = \frac{-400 \, \text{kJ}}{100 \, \text{K}}
\]

First, we convert kJ to J:

\[
-400 \, \text{kJ} = -400,000 \, \text{J}
\]

Now we substitute:

\[
\Delta S_{\text{surroundings}} = \frac{-400,000 \, \text{J}}{100 \, \text{K}} = -4000 \, \text{J/K} = -4 \, \text{kJ/K}
\]

Thus, the change in entropy of the surroundings is:

\[
\Delta S_{\text{surroundings}} = -4 \, \text{kJ/K}
\]

The correct answer from the choices given is:

**- 4 kJ/K**