Question

question 7
1 pts
calculate the magnitude of w, in kj, for a system that releases 4.42×10³ j of heat to its surroundings and for which the change in total internal energy is 9.9 kj. report your answer to one place past the decimal
point.
1 pts

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, and $w$ is the work.
Since the system releases heat, $q=- 4.42\times10^{3}\text{ J}=-4.42\text{ kJ}$ (because $1\text{ kJ} = 10^{3}\text{ J}$), and $\Delta U = 9.9\text{ kJ}$.

Step2: Rearrange the formula to solve for $w$

Rearrange $\Delta U=q + w$ to $w=\Delta U - q$.
Substitute the values: $w=9.9\text{ kJ}-(-4.42\text{ kJ})$.

Step3: Calculate the value of $w$

$w=9.9\text{ kJ}+4.42\text{ kJ}=14.32\text{ kJ}\approx14.3\text{ kJ}$ (rounded to one decimal place).

Answer:

$14.3$