You would like to freeze a surgically removed 5.0 cm diameter spherical brain tumor. in order to avoid the formation of large ice crystals within the tumor, you would like to keep the temperature within the tumor spatially uniform. tissue properties: constant thermal conductivity = 0.64 w/m*k, thermal diffusivity = 2.5 x 10-7 m2/s. (a) determine an appropriate h in order to meet this criteria. (b) how long will the tumor take to freeze, i. e. reach 0°c, if placed in a -20°c freezer using the h found in part (a).

In a thunderstorm, charge builds up on the water droplets or ice crystals in a cloud. thus, the charge can be considered to be distributed uniformly throughout the cloud. for the purposes of this problem, take the cloud to be a sphere of diameter 1.00 kilometer. the point of this problem is to estimate the maximum amount of charge that this cloud can contain, assuming that the charge builds up until the electric field at the surface of the cloud reaches the value at which the surrounding air breaks down. this breakdown means that the air becomes highly ionized, enabling it to conduct the charge from the cloud to the ground or another nearby cloud. the ionized air will then emit light due to the recombination of the electrons and atoms to form excited molecules that radiate light. in addition, the large current will heat up the air, resulting in its rapid expansion. these two phenomena account for the appearance of lightning and the sound of thunder. take the breakdown electric field of air to be eb=3.00ă—106n/c. part a estimate the total charge q on the cloud when the breakdown of the surrounding air is reached. express your answer numerically, to three significant figures, using ďµ0=8.85ă—10â’12c2/(nâ‹…m2) .

For the car in the picture ,in which direction is the normal force? -into the screen -down -out of the screen -up

Anoche fuimos al restaurante el gusto. jaime le (1) (pedir) al camarero una mesa en la sección de no fumar. yo (2) (pedir) chuleta de cerdo con champiñones, papas y ensalada y jaime (3) (pedir) mariscos, arroz y ensalada. el restaurante estaba lleno (full) por eso no nos (4) (servir) muy rápido (very fast), pero la comida estaba deliciosa. no me lo vas a creer (you won't believe it) pero ¡jaime (5) (repetir) arroz y mariscos! ¡dos porciones (orders)! ¿ya entiendes por qué él no (6) (dormir) bien anoche?