As a rule of thumb in a smoke alarm, alkaline batteries will last for about 1-2 years and Lithium batteries for 6 years plus

For instance, a carbon zinc battery in a BRk 9120B will last up to one year. It all depends on how fresh it was before it was installed and when the unit itself was activated. UL 217 mandates that any installed battery in a backup mode only alarm needs to last at least for 24 hours in standby condition and thereafter be able to be in alarm for at least 4 minutes. As a rule of thumb in a smoke alarm, alkaline batteries will last for about 1-2 years and Lithium batteries for 6 years plus.