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SPSolution14-16

SPSolution14-16 - Naik Sameer V Solution for Special...

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Naik, Sameer V. Fall 2009 1000 Solution for Special Problem 14 Given: - Automobile tire with known volume Find: - Change in tire pressure (kPa) when air temperature increases from 25 ° C to 50 ° C - Amount of air (kg) to be bled off from the tire to restore original pressure System: Assumptions: - Automobile tire is a closed system (mass constant) - Tire volume is constant - Air behaves as an ideal gas Basic Equation(s): PV mRT = Solution: (a) From Table A-1, the critical pressure and temperature for air are 3.77 MPa and 133 K, respectively. Hence, at the initial condition: ( ) 1 ,1 25 273.15 K 2.24 133 K R cr T T T + = = = and 1 ,1 0.31 MPa 0.0822 3.77 MPa R cr P P P = = = From Fig. A-1, the compressibility factor is approximately 1; the assumption of ideal gas behavior for air is appropriate. Since mass of air remains constant, we can write: 1 1 2 2 1 2 PV PV m RT RT = = . However, the tire volume is constant ° ( ) ( ) 1 2 2 2 1 1 2 1 50 273.15 K 310 kPa 336 kPa 25 273.15 K P P T P P T T T + = ° = = × = + Hence, the change in tire pressure when the air temperature increases from 25 ° C to 50 ° C is: 2 1 P P P Δ = - i.e.
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