Question

If $\Delta U = 100\text{ J}$ and work done = $40\text{ J}$, heat supplied is:

• A. $60\text{ J}$
• B. $140\text{ J}$
• C. $100\text{ J}$
• D. $40\text{ J}$

Hint:

Always pay close attention to sign conventions in thermodynamics.
Heat supplied to the system is positive (+), and heat rejected is negative (-).
Work done by the system is positive (+), and work done on the system is negative (-).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question is based on the application of the First Law of Thermodynamics, which is a statement of the law of conservation of energy.
The first law establishes a relationship between heat supplied, work done, and change in internal energy of a system during a thermodynamic process.

Step 2: Key Formula or Approach:
The governing relationship is given by the expression:
\[ \Delta Q = \Delta U + W \] Where:
$\Delta Q$ is the net heat supplied to the system.
$\Delta U$ is the change in internal energy of the system.
$W$ is the work done by the system.

Step 3: Detailed Explanation:

• The change in internal energy is given as $\Delta U = 100\text{ J}$. This positive value represents an increase in the internal energy of the system.

• The work done by the system is given as $W = 40\text{ J}$. This positive value indicates work is being performed by the system on its surroundings (expansion work).

• Substituting these values into the first law equation:
\[ \Delta Q = 100\text{ J} + 40\text{ J} = 140\text{ J} \]
• The resulting positive value of $140\text{ J}$ indicates that heat is supplied to the system.

Step 4: Final Answer:
The heat supplied to the system is $140\text{ J}$, which corresponds to option (B).