What is the root mean square speed of nitrogen molecules in air at 300 K ? of ox

Question

What is the root mean square speed of nitrogen molecules in air at 300 K ? of oxygen molecules? If we increase the temperature of a gas from 300 K to 600 K, by what factor do we increase the rms speed of its molecules? The complete metabolization of one apple supplies 110 kcal of chemical energy. How high can you climb up a hill on this amount of energy? Assume that your muscles can completely convert the chemical energy into mechanical energy. Also assume your mass is 75 kg. The highest tower in the world is the steel radio mast of Warsaw Radio in Poland which is 646 m high. How much does this height increase between a cold winter day when the temperature is - 35 degree C and a hot summer day when the temperature is +35 degree C? A glass vessel of volume 200 cm^3 is filled to the rim with mercury. How much of the mercury will overflow the vessel if the temperature is raised by 30 degree C? beta_mercury = 0.182 times 10^-3/degree C, beta_glass = 2.7 times 10^-5/degree C. Suppose that when we heat an aluminum rod, its length increases by 0.02%. What is the corresponding percent increase of the volume of the rod? A house is built of bricks, with walls 20 cm thick. The wall in one of the rooms of this house measures 5.0 m times 3.0 m. What is the heat flow through this wall if the inside temperature is 21 degree C and the outside temperature -18 degree C? Thermal conductivity k = 0.63 J/(s.m. degree C) The walls of houses built in Northeastern United States are commonly insulated with 6 in (15 cm) of fiberglass insulation. If you want to get the same insulation with hardwood walls, what should be the thickness of the wood? k_glass = 0.042 J/(s.m. degree C), k_wood = 0.13 J/(s.m. degree C) A piece of ice at 0 degree C is in contact with a piece of steel. If heat is flowing from the ice to the steel, what can you say about the temperature of the steel? Correlate beta, the coefficient of volume (thermal) expansion of a solid with alpha, the coeff., of linear expansion. How much heat is needed to take ice of mass m = 720 g at - 10 degree C to a liquid state at 15 degree C? Define heat capacity. How is heat capacity different from specific heat? Early in the morning at the beginning of a trip, tires of an automobile are cold (280 K), and their air is at a pressure of 3.0 atm. Later in the day, after a long trip on hot streets, the tires are hot (330 K). What is the pressure? Assume that the volume of the tires remains constant. (To discuss about absolute and gauge pressure.

Explanation / Answer

5

rms speed is given by

v=sqrt(3RT/M)

T=300 K

for N2,M=28

v=16.34 m/s

for O2,M=32

v=15.3 m/s

6

As seen v varies sqrt(T) so if T doubles v will be increased by sqrt(2) times i.e. 1.414 times

7

conserving energy

mgh=Energy (in joules)

75*9.8*h=110*1000*4.184

h=626.2 m

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