During compression of a spring the work done is $10\,kJ$ and $2\,kJ$ escaped to the surroundings as heat. The change in internal energy, $\Delta\, U(in\,kJ)$ is:

Question

Which is an adiabatic process?

Answer 1

To find the change in internal energy during the compression of a spring, we need to apply the first law of thermodynamics. The first law is mathematically given by the formula:

$\Delta U = Q - W$

where:

$\Delta U$ is the change in internal energy,
Q is the heat exchanged with the surroundings, and
W\) is the work done on or by the system.

In this context:

The work done on the spring (which is work done by the system) is 10\,kJ because the spring is compressed.
The heat escaped to the surroundings is 2\,kJ.

Since the work is done on the system, it is considered positive, and since the heat is lost to the surroundings, it is considered a negative value. Therefore, substituting these values into the equation gives:

$\Delta U = -2\,kJ - 10\,kJ$

$\Delta U = -2 -(-10)$

Upon calculating:

$\Delta U = 8\,kJ$

Therefore, the change in internal energy is 8 kJ. This matches the correct answer option, which is 8.

Answer 2