To solve this problem, we need to determine the change in internal energy (ΔU) of the system during the compression of a spring. The key principle here is the First Law of Thermodynamics, which states:

$\Delta U=q+w$

where:

• ΔU is the change in internal energy,
• q is the heat exchanged with the surroundings,
• w is the work done on or by the system.

Now, let's analyze the given data:

• Work done on the system (compression) is 10 kJ. Since work is done on the system, it is positive: $w=+10\mathrm{kJ}$.
• Heat escaped to the surroundings is 2 kJ. Since heat is lost by the system, it is negative: $q=-2\mathrm{kJ}$.

Substitute these values into the First Law equation:

$\Delta U=q+w=(-2)+(+10)=8\mathrm{kJ}$

Therefore, the change in internal energy is +8 kJ.

Final Answer: 8

Related Topics and Formulae

First Law of Thermodynamics: This law is a statement of conservation of energy. It asserts that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings (or plus the work done on the system). The standard form is $\Delta U=q+w$, where the sign conventions are crucial:

• q (heat): Positive when heat is absorbed by the system. Negative when heat is released by the system.
• w (work): Positive when work is done on the system (e.g., compression). Negative when work is done by the system (e.g., expansion).

Internal Energy (U): It is the total energy contained within a system, encompassing both kinetic and potential energy at the molecular level. For ideal gases and many processes, changes in internal energy (ΔU) are often related to changes in temperature.

Work in Thermodynamics: In the context of gases, work is often calculated as $w=-P_{\text{ext}}\Delta V$. For processes like spring compression, work is given directly, as in this problem.