Question

An electric heater supplies heat to a system at a rate of 100 W. If the system performs work at a rate of 75 W, then the rate at which internal energy increases will be: ____.

• A. 125 W
• B. 75 W
• C. 100 W
• D. 25 W

Hint:

Internal energy is like a bank account. If you put in \$100 (heat) but spend \$75 (work), your balance (internal energy) only increases by \$25.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The First Law of Thermodynamics states that the heat added to a system is equal to the change in its internal energy plus the work done by the system. When dealing with "rates" (Watts), the law still holds.

Step 2: Key Formula or Approach:
\[ \frac{dQ}{dt} = \frac{dU}{dt} + \frac{dW}{dt} \]

Step 3: Detailed Explanation:
Given: - Rate of heat supply ($\frac{dQ}{dt}$) = 100 W - Rate of work done ($\frac{dW}{dt}$) = 75 W 1. Rearrange the formula to find the rate of change of internal energy ($\frac{dU}{dt}$): \[ \frac{dU}{dt} = \frac{dQ}{dt} - \frac{dW}{dt} \] 2. Substitute the values: \[ \frac{dU}{dt} = 100 - 75 = 25 \text{ W} \]

Step 4: Final Answer:
The rate at which internal energy increases is 25 W.