The problems of the first law
1.  a lead bullet is fired at a frigid surface. At what speed must it travel to melt on impact, if its initial temperature is 25℃ and heating of the rigid surface of the rigid surface is neglected? The melting point of lead is 327℃. The molar heat of fusion of the lead is 4.8kJ/mol. The molar heat capacity CP of lead may be taken as 29.3J/(mol K)  (1.1)
Solution:
2. what is the average power production in watts of a person who burns 2500 kcal of food in a day? Estimate the average additional powder production of 75Kg man who is climbing a mountain at eh rate of 20 m/min  (1.2)
Solution
3 One cubic decimeter (1 dm3) of water is broken into droplets having a diameter of one micrometer (1 um) at 20℃.  (1.3)
(a)what is the total area of the droplets?
(b)Calculate the minimum work required to produce the droplets. Assume that the droplets are rest (have zero velocity)
Water have a surface tension of 72.75 dyn/cm at 20℃ (NOTES: the term surface energy (ene/cm2) is also used for surface tension dyn/cm)
Solution
4.Gaseous helium is to be used to quench a hot piece of metal. The helium is in storage in an insulated tank with a volume of 50 L and a temperature of 25℃, the pressure is 10 atm. Assume that helium is an ideal gas.
(a)when the valve is opened and the gas escapes into the quench chamber (pressure=1 atm), what will be the temperature of the first gas to hit the specimen?
(b)As the helium flows, the pressure in the tank drops. What will be the temperature of the helium entering the quench chamber when the pressure in the tank has fallen to 1 atm? (1.4)
Solution:
5 An evacuated (P=0), insulted tank is surrounded by a very large volume (assume infinite volume) of an ideal gas at a temperature T0. The valve on the tank is opened and the surrounding gas is allowed to flow quickly into the tank until the pressure inside the tank is equals the pressure outside. Assume that no heat flow takes place. What is the final tempeture of the gas in the tank? The heat capacity of the gas, Cp and Cv each may be assumed to be constant over the temperature rang spanned by the experiment. You answer may be left in terms of Cp and Cv
hint: one way to approach the problem is to define the system as the gas ends up in the tank. (1.5)
solution
6. Calculate the heat of reaction of methane with oxygen at 298K, assuming that the produ
cts of reaction are CO2 and CH4 (gas)[This heat of reaction is also called the low calorific power of methane] convert the answer into unites of Btu/1000 SCF of methane. SCF means standard cubic feet, taken at 298 and 1atm
NOTE: this value is a good approximation for the low calorific powder of natural gas (1.6)
DATA:      
solution
7. Methane is delivered at 298 K to a glass factory, which operates a melting furnace at 1600 K. The fuel is mixed with a quantity of air, also at 298 K, which is 10% in excess of the amount theoretically needed for complete combustion (air is approximately 21% O2 and 79
% N2) (1.7)
(a)Assuming complete combustion, what is the composition of the flue gas (the gas following combustion)?
(b)What is the temperature of the gas, assuming no heat loss?
(c)The furnace processes 2000kg of glass hourly, and its heat losses to the surroundings average 400000 kJ/h. calculate the fuel consumption at STP (in m3/h) assuming that for gas H1600-H298=1200KJ/KG
(d)A heat exchanger is installed to transfer some of the sensible heat of the flue gas to the combustion air. Calculate the decrease in fuel consumption if the combustion air is heated to 800K
DATA STP means T=298K, P=1atm
   
Solution
8.In an investigation of the thermodynamic properties of a-manganese, the following heat contents were determined:
H700-H298=12113 J/(g atom)
H1000-H298=22803 J/(g atom)
Find a suitable equation for HT-H298 and also for CPreaction in the shaft as a function of temperature in the form (a+bT) Assume that no structure transformation takes place in the given tempeture rang. (1.8)

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