Suppose that the laptop is placed in an insulating briefcase with a fully charged battery, but it does not go into “sleep” mode, and the battery discharges as if the laptop were in use. If no heat leaves the briefcase, the heat capacity of the briefcase itself is negligible, and the laptop has a mass of 2.3 kg and an average specific heat of 0.8 kJ? kg?1? °C?1, estimate the temperature of the laptop after the battery has fully discharged.

Question

The battery in a laptop computer supplies 11.1 V and has a capacity of 56 W? h. In ordinary use, it is discharged after 4 hours. What is the average current drawn by the laptop, and what is the average rate of heat dissipation from it? You may assume that the temperature of the computer remains constant.

Answer 1

If we take the laptop and bag as the system, then there is no exchange of heat or work between the system and surroundings, and the first law tells us that ?Ut = 0. The internal energy does not change, but the chemical energy stored in the battery is released as sensible heat, which raises the temperature of the computer. The total amount of energy stored in the battery is 56 W? h = 56 J/s? h? 3600 s/h = 201600 J = 201.6 kJ. The total heat capacity of the laptop is 2.3? 0.8 = 1.84 kJ/K. Thus, energy release of 201.6 kJ would increase the temperature by 201.6 kJ/1.84 kJ/K = 110 K = 110°C (because this is a temperature DIFFERENCE, and not an absolute temperature, units of K and °C are the same). If the computer started off at a cool 20°C, the estimated final temperature is 130°C
(about 270°F). At that point, the foam briefcase would probably start melting onto the surface of the laptop. Fortunately, in real life, this is unlikely to happen, and even if it did, the bag would not be perfectly insulating. Nonetheless, a typical laptop battery does store sufficient energy to cook the laptop in which it is installed if no heat could be removed.