A system does 200 J of work and at the same time absorbs 150 J of heat. The magnitude of the change

Q: Why is work taken as negative when the system does it?

In chemistry, we focus entirely on the system's perspective. If the system does work on the surroundings (like expanding against atmospheric pressure), it uses up its own energy. Since energy is leaving the system, we denote it with a negative sign.

Q: What if I use the physics sign convention?

In physics, the first law is often written as $\Delta U = q - W$, where $W$ is defined as the work done BY the system (making $W$ positive in this case). If you plug in $q = 150$ and $W = 200$, you get $\Delta U = 150 - 200 = -50\text{ J}$. The final result for $\Delta U$ is exactly the same!

Q: Does 'magnitude' mean I just ignore the negative sign?

Yes, magnitude refers to the absolute value. It represents the sheer size of the change, regardless of whether it was an increase (positive) or a decrease (negative).

Q: What does a negative $\Delta U$ imply physically?

A negative $\Delta U$ means the system lost energy overall. For an ideal gas, internal energy is directly proportional to temperature, so a negative $\Delta U$ would mean the gas cooled down.

Q: Is internal energy a state function?

Yes! $\Delta U$ depends only on the initial and final states of the system, not on the specific path taken or how the heat and work were individually exchanged.

Question

A system does $200	ext{ J}$ of work and at the same time absorbs $150	ext{ J}$ of heat. The magnitude of the change in internal energy is ......... $	ext{J}$. (Nearest integer)

Sigma Percentile · Accepted Answer

### The First Law of Thermodynamics: Balancing Heat and Work

Imagine a gas trapped inside a cylinder with a movable piston. This gas is our **thermodynamic system**. The universe is constantly exchanging energy with this system in two primary ways: through heat and through work.

In this problem, we are told that the system absorbs $150	ext{ J}$ of heat. According to the IUPAC sign convention used in chemistry, any energy entering the system is considered positive. Therefore, the heat exchanged is $q = +150	ext{ J}$.

At the exact same time, the system does $200	ext{ J}$ of work. When a system does work (like expanding and pushing a piston upward), it expends its own energy. Because energy is leaving the system, we assign a negative sign to this work. Thus, $W = -200	ext{ J}$.

### The Master Equation

To find out what happens to the system's overall energy, we invoke the **First Law of Thermodynamics**. This law is essentially the principle of conservation of energy applied to thermodynamic systems. It states that the change in internal energy ($\Delta U$) is the sum of the heat added to the system and the work done on the system.

Mathematically, it is expressed as:

$$\Delta U = q + W$$

### Final Calculation

Now, we carefully substitute our values into the master equation. It is crucial to carry the signs along to avoid silly mistakes!

$$\Delta U = (+150	ext{ J}) + (-200	ext{ J})$$

$$\Delta U = -50	ext{ J}$$

The negative sign indicates that the system's internal energy has decreased by $50	ext{ J}$ overall. It spent more energy doing work than it gained from the heat it absorbed.

However, the question specifically asks for the **magnitude** of the change in internal energy. The magnitude is simply the absolute value, stripping away the sign to just look at the 'size' of the change.

$$|\Delta U| = |-50	ext{ J}| = 50	ext{ J}$$

And there we have it! The magnitude of the change in internal energy is **$50	ext{ J}$**.

Animated Solution for Chemistry - Chemical Thermodynamics: A system does $200 J$ of work and at the same time absorbs $150 J$ of heat. The magnitude of the change in internal energy is ......... $J$ . (Nearest integer)

Enter Numerical Value:

Visualized Solution

$q, W$

$Δ U = q + W$

$Δ U = (+ 150) + (- 200)$

$Δ U = - 50 J$

|\Delta U| = 50 \text{ J}

W_{\text{on system}} > 0

The Sigma Insight: First Law of Thermodynamics

The First Law of Thermodynamics

The Master Equation

Final Calculation

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