Question

calculate the magnitude of w, in kj, for a system that absorbs 2.48×10³ j of heat from its surroundings and for which the change in total internal energy is -28.7 kj. report your answer to one place past the decimal point.

Explanation:

Step1: Recall the first law of thermodynamics

The first law of thermodynamics is $\Delta U = q+w$, where $\Delta U$ is the change in internal energy, $q$ is the heat absorbed, and $w$ is the work done.
Given $q = 2.48\times10^{3}\text{ J}=2.48\text{ kJ}$ and $\Delta U=- 28.7\text{ kJ}$.

Step2: Rearrange the formula to solve for $w$

Rearrange $\Delta U = q + w$ to $w=\Delta U - q$.
Substitute the values: $w=-28.7\text{ kJ}-2.48\text{ kJ}$.

Step3: Calculate the value of $w$

$w=-28.7 - 2.48=-31.18\text{ kJ}$. Rounding to one decimal place, $w=-31.2\text{ kJ}$. The magnitude of $w$ is $|w| = 31.2\text{ kJ}$.

Answer:

$31.2$