Calculate the change in internal energy of the following system: A balloon is cooled by removing 0.657 kJ of heat. it shrinks on cooling, and the atmosphere does 385 J of work on the balloon.

Question

Express your answer to three significant figures and include the appropriate units.

Answer 1

To calculate the change in internal energy of the system, we can use the first law of thermodynamics, which is given by the equation:

\[ \Delta U = Q - W \]

where:

• \(\Delta U\) is the change in internal energy,
• \(Q\) is the heat added to the system (negative when heat is removed),
• \(W\) is the work done by the system (positive when work is done on the system).

In this case:

• The system (the balloon) loses heat, so \(Q = -0.657 \text{ kJ} = -657 \text{ J}\) (since \(1 \text{ kJ} = 1000 \text{ J}\)).
• The atmosphere does work on the balloon, \(W = -385 \text{ J}\) (because work is done on the system).

Now we can plug these values into the equation:

\[ \Delta U = Q - W = (-657 \text{ J}) - (-385 \text{ J}) \]

This simplifies to:

\[ \Delta U = -657 \text{ J} + 385 \text{ J} = -272 \text{ J} \]

Now, we express the result in three significant figures:

\[ \Delta U = -272 \text{ J} \]

Thus, the change in internal energy of the system is:

\[ \Delta U = -272 \text{ J} \]