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: Understanding the Question:
We are given a thermodynamic process where a system absorbs a specific amount of heat energy ($54\ \mathrm{J}$) and performs an amount of work ($238\ \mathrm{J}$) on its surroundings. We need to determine the net change in internal energy ($\Delta U$).

Step 2: Key Formula or Approach:
According to the first law of thermodynamics, the mathematical relationship is: $$\Delta U = Q + W$$ Using standard sign conventions in chemistry:

• Heat absorbed by the system is positive: $Q = +54\ \mathrm{J}$.

• Work done by the system on the surroundings is negative: $W = -238\ \mathrm{J}$.

Step 3: Detailed Explanation:
Substitute the given values along with their correct thermodynamic signs into the first law formula: $$\Delta U = 54\ \mathrm{J} + (-238\ \mathrm{J})$$ $$\Delta U = 54 - 238 = -184\ \mathrm{J}$$ The negative value indicates that the internal energy of the system decreases because it expended more energy performing work than it absorbed as heat.

Step 4: Final Answer:
The change in internal energy of the system is $-184\ \mathrm{J}$, which corresponds to option (D).