Question

If a system has 475 kcal of work done to it, and releases 5.00 × 102 kJ of heat into its surroundings, what is the change in internal energy of the system?

Answer 1

First, we convert kcal to joules:
1 kcal = 4.184 kJ
475 kcal = 1987.4 kJ

Now, calculating the change in internal energy:

ΔU = Q + W; where Q is the heat supplied to the system and W is the work done on the system.

ΔU = -500 + 1987.4
ΔU = 1487.4 kJ

Answer 2

The change in the internal energy of the system due to the work done and the heat released is $\boxed{1487.4\,{\text{kJ}}}$.

Further Explanation:

Given:

The energy absorbed by the system from the surroundings is $5.0\times {10^2}\,{\text{kJ}}$.

The work done by the surroundings on the system is $475\,{\text{kcal}}$.

Concept:

The change in internal energy of the system due to the amount of work done and the amount of energy released by the system into the surroundings is given by the First Law of Thermodynamics.

According to the First Law of Thermodynamics, the energy of an isolated system is always conserved. It means that the change in internal energy of the system is equal to the sum of the work done on the system and the amount of energy absorbed by the system.

$\Delta U = Q + W$

Here, $\Delta U$ is the change in internal energy, $Q$ is the energy absorbed and $W$ is the work done.

Here the value of $Q$ will be negative because the system does not absorb any energy. It rather releases energy into the surroundings.

The amount of work done on the system in Joules is:

$\begin{aligned}475\,{\text{Kcal}} &= 475 \times 4.184\,{\text{kJ}}\\&= {\text{1987}}{\text{.4}}\,{\text{kJ}}\\\end{aligned}$

Substitute the value in above expression.

$\begin{aligned}\Delta U&= - 500\,{\text{kJ}} + 1987.4\,{\text{kJ}}\\&= 1487.4\,{\text{kJ}}\\\end{aligned}$

Thus, the change in the internal energy of the system is $\boxed{1487.4\,{\text{kJ}}}$.

Learn More:

1. One consequence of the third law of thermodynamics is that brainly.com/question/3564634

2. Calculate the average translational kinetic energy brainly.com/question/9078768

3. According to Charles’s law, for a fixed quantity of gas at constant pressure brainly.com/question/7316997

Answer Details:

Grade: College

Subject: Physics

Chapter: Heat and Thermodynamics

Keywords:

System released, heat into its surroundings, work done, energy absorbed, change in internal energy, first law of thermodynamics.