Question

In a process, a system performs $238\ \mathrm{J}$ of work on it's surrounding by absorbing $54\ \mathrm{J}$ of heat. What is the change in internal energy of system during this operation?

• A. $222\ \mathrm{J}$
• B. $-192\ \mathrm{J}$
• C. $54\ \mathrm{J}$
• D. $-184\ \mathrm{J}$

Hint:

Always double-check your signs: "Absorbing heat" is $+Q$, while "performing work on surroundings" is $-W$. Simply combine them directly: $\Delta U = Q_{\mathrm{in}} - W_{\mathrm{out}} = 54 - 238 = -184\ \mathrm{J}$.

Answer 1

The Correct Option is D

Step 1: Write the first law.
The change in internal energy is $\Delta U = Q + W$, where signs carry the physical meaning.
Step 2: Fix the sign of heat.
The system absorbs heat, so heat flows in and $Q = +54\ J$.
Step 3: Fix the sign of work.
The system does work on the surroundings, so energy leaves as work and $W = -238\ J$.
Step 4: Substitute into the law.
\[ \Delta U = (+54) + (-238). \]
Step 5: Do the arithmetic.
$\Delta U = 54 - 238 = -184\ J$.
Step 6: Interpret the sign.
The negative result means internal energy falls, because the system spent more energy on work than it gained as heat.
\[ \boxed{-184\ J \text{ (option D)}} \]