Disclosed is a power supply device including a battery having an exhaust valve that opens when an internal pressure becomes higher than a set pressure, the battery being housed in a case, a temperature sensor that detects a temperature in the case, and a detection circuit that detects opening of the exhaust valve at a detected temperature detected by the temperature sensor. In this power supply device, the detection circuit detects that a high temperature time (t1) from a timing at which a rate of rise (ΔT/Δt) of the temperature detected by the temperature sensor is higher than a rise rate set value and exceeds the rise rate set value to a timing at which the detected temperature falls to less than or equal to a reference temperature is longer than a high temperature time set value, and detects the opening of the exhaust valve.