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hw1_solutions

# hw1_solutions - ES330 Assignment 1 Solutions Chapters 2 and...

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ES330 Assignment 1 Solutions Chapters 2 and 3 Due Date: Thursday September 2, 2010 1 Similar to Problem 2-7 in Text The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25 o C , the pressure gage reads 225 kPa . If the volume of the tire is 0.035 m 3 , determine the pressure rise in the tire when the air temperature in the tire rises to 55 o C . Also, determine the amount of air that must be bled off to restore pressure to its original value at this temperature. Assume the atmospheric pressure to be 100 kPa . Solution (1) Find the Change in Pressure: We can assume the air behaves ideally under these conditions, and can therefore apply the Ideal Gas Law: = RT (1) ν = RT 1 P 1 = RT 2 P 2 (2) Here, ν is the specific volume. This is assuming that the volume of the tire does not change with varying temperature. We can now simplify the equation to: T 1 P 1 = T 2 P 2 (3) The temperatures must be converted into Kelvin to obtain the correct solution: T 1 =25 o C + 273.15 = 298.15K T 2 =55 o C + 273.15 = 328.15K The pressure must be converted from gage to absolute: P 1 ,atm = P 1 ,gage + P atm =225 kPa +100 kPa =325 kPa Therefore, solving for P 2 in Equation 3: P 2 = P 1 T 2 T 1 = (325 kPa )(328 . 15 K ) 298 . 15 K = 358 kPa (4) To get the pressure change: ΔP= P 1 - P 2 = 358 kPa - 325 kPa ΔP=33 kPa 1

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(2) Determine How Much Air Should be Released to Restore 225 kPa : To determine how much air should be released, the original mass in the tire must be calculated. This can be done by applying the ideal gas law to calculate the mass (either at 25 o C and 325 kPa or at 55 o C and 358 kPa ). The gas constant for air is also needed: R air = 0 . 2870 kJ Kg * K = 0 . 2870 kPa * m 3 Kg * K
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