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1. A sphere of radius R contains water. If you make a small hole of radius r at

ID: 1659244 • Letter: 1

Question

1. A sphere of radius R contains water. If you make a small hole of radius r at the bottom derive the time that it would taketo empty the sphere if R = 1 m and r =01 m, calculate the time. 2. Use the conservation of momentum principle to calculate the individual kinetic energy of a gas molecule. Find the rms velocity of a nitrogen molecule if the room temperature is 27 degree Celsius. 3. Derive the mean free time and mean free path of a gas molecule. Calculate both these parameters for a nitrogen molecule at T = 27 degree Celsius. 4. Derive the expression for the rms velocity using the Maxwell-Boltzmann distribution. S. Prove that the integral of M-B distribution from zero to infinity is 1. What will be the fraction of nitrogen molecules at T-300 K that will have velocities between 100 m/s and 200 m/s? .0. You have decided to freeze water in your freezer. There are 16 small containers in a 10 cmx 20 cm tray with a depth of 3 cm. If the freezer temperature is -10 degree Celsius and the water temperature- initially - was 20 degree Celsius, find the time it will take to freeze the water completely. Assume the heat escapes only through the top of the water surface. A steel pendulum clock of length 1 m gives correct time at T-20 Celsius. Find the maximum (or minimum) temperature that can be allowed so that the clock does not run more than 4 second fast or slow in a day. Assume when an air molecule strikes your body it gives up all its energy. Calculate the number of air molecules needed to raise your body temperature by 1 degree. Assume your body mass to be 50 kg and consisting of water. -23 m.K K: 2.18 w 1o "27 water re 3.33 /0'

Explanation / Answer

Given that

body contains of water of mass M = 50 kg

heat capacity of water C = 4184 J/ kg k

the temperature raise is DT = 1 degree

we know that from the definition of heat capacity

the amount of heat energy required for one kg fo mass through one degree raise in temperature .

that is

C = Q/m*DT

Q = m*C*DT

Q = 50*4148*1 J

Q = 207400 J

the no of air molecules required to raise the temperature is  

N = 207400/( energy given out by each air molecule up on striking the body)