Assume the bag is sitting in the back seat of a field vehicle. The gas in the bag expands reversibly and isothermally as we ascend the mountain. This is the reversible path - it is important to us because the system never deviates by more than an infinitesimal amount from an equilibrium state. This is the second law. So, the gas expands and hence cools.
Irreversibility tends to reduce the magnitude of the temperature decrease.