In a closed system with 500 J in the kinetic energy store and 200 J in the thermal energy store, 100 J is transferred from kinetic to thermal; what is the total energy of the system now?

What this question is testing

Because the system is described as closed, energy cannot enter or leave the system. A transfer between stores changes how the energy is shared, not the total amount.

Update each energy store after the transfer

• Kinetic store starts at $500\,\text{J}$ and loses $100\,\text{J}$: $$500 - 100 = 400\,\text{J}$$
• Thermal store starts at $200\,\text{J}$ and gains $100\,\text{J}$: $$200 + 100 = 300\,\text{J}$$

Add to find the total energy now

$$E_{\text{total}} = 400\,\text{J} + 300\,\text{J} = 700\,\text{J}$$ So the total energy of the closed system is unchanged at $700\,\text{J}$.