Final answer:
The depreciation expense for the third year of a piece of machinery that depreciates at $1,500 annually is $1,500.
Step-by-step explanation:
To record the depreciation expense for the third year for a piece of machinery that was originally purchased for $10,000 and depreciates at $1,500 annually, one needs to calculate the cumulative depreciation for the first two years and then apply the third year's depreciation. Since the depreciation is uniform each year, the third year's depreciation would still be $1,500. Therefore, the journal entry would be to debit Depreciation Expense for $1,500 and to credit Accumulated Depreciation for $1,500.