1. PHY 126-07 Mid-term Exam II Problem 1 (10+10 points) Chapters 15,16,17,18 A scientist is making a mockup model of a human ear using a small can with the top surface open and the bottom closed. A human ear is especially sensitive to sound whose frequency is 3,440 Hz. If this is the lowest frequency that the ear is especially sensitive to, (a) what the height of the mockup model h should be? Assume that the speed of sound is 344 m/s. (b) What is the next lowest frequency the ear especially sensitive to? You need to write how you have derived the answers. Just writing an answer does not get you the full point. When you use symbols that you define, make clear what these symbols represent. open closed h

2. Problem 2 (3+3+3+3+3+5 points) 6.00 kg of ice at -5.00 o C is added to a cooler holding 30 liters of water at 20.0 o C. The density of water is 1000 kg/m 3. The latent heat of fusion of water L L is 3.33 x 10 5 J/kg, the specific heat of water c water and ice c ice are 4190 and 2090 J/(kg K), respectively. (a)What is the mass of 30-liter water m water ? (b)To melt 6.00 kg of ice how much heat Q melt is needed? (c)To change the temperature of the ice to 0.00 o C how much of heat Q ice is needed? (d)Once all the ice melts how much of heat Q ice-water is needed to raise the temperature of the water from the ice to T? (e)To lower the temperature of 30 liter water from 20.0 o C to T, how much heat Q water is needed? (f)What temperature of the water T when it comes to equilibrium?

3. Problem 3 (4+4+4+4+4 points) A hot-air balloon stays aloft because hot air at atmospheric pressure is less dense than cooler air at the same pressure. If the volume of the balloon is V=500 m 3 and the surrounding air is at T=15.0 o C, you will find the temperature of the air in the balloon be for it to lift a total load m=290 kg (in addition to the mass of the hot air). The density of air at T=15.0 o C and atmospheric pressure is  = 1.23 kg/m 3. Ignore the weight of balloon’s skin. Answer the following questions: (a)Find the buoyant force B by the air in the atmosphere in terms of V,  and g? (b)What must the density of the hot air  ’ be for the balloon and the load to float in the atmosphere in terms V, , and m? (c)From the ideal gas equation pV=nRT, derive the relation  T= constant at a constant pressure. (d)If the temperature of the hot air is T’, express T’ by T, , and  ’. (e)Express T’ in terms of T, , m and V. (f)Plug-in all the numerical values needed and find the temperature of the hot air.