Question

There was transfer of energy of 5000 J into a system due to a temperature difference, and the entropy increased by 10 J/K. What was the approximate temperature of the system, assuming that the temperature didn’t change very much?.

Short answer

• The approximate temperature of the system is $500\text{K}$

Step-by-step solution

Identification of given data

• The energy transferred is$Q=5000\text{J}$.
• The increase in entropy is$S=10\text{J/K}$.

Concept of entropy

A condition of disorder, unpredictability, or uncertainty is usually related to the scientific notion of entropy, which is also a physical characteristic that can be measured.

The entropy of a system is given by,

$S=\frac{Q}{T}$…… (i)

Here $Q$is the energy transfer of the system.

$T$is the temperature change of the system.

Determination of the change in temperature

The change in temperature can be evaluated using equation $\left(i\right),$

$$\begin{gathered} 10J/K=\frac{5000J}{T} \\ T=\frac{5000}{10}·\frac{1J}{1J/K} \\ T=500\left(1K\right) \\ T=500K \end{gathered}$$

Thus, the change in temperature of the system is found to be $500\text{K}$.