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ENGR5003 / Week 1
Old spec Tutorial 1 Problem 2TutorialOld spec ENGR217Third8 min

ENGR217 (old spec) Thermo L6 Tutorial 1, Problem 2 official answers

The pressure in a car tyre depends on the temperature of the air in the tyre. When the air temperature is 10 C, the gauge pressure is 2.4 bar. The tyre creates an internal volume of 0.025 m3\mathrm{m^3} against the wheel and this volume is independent of pressure. Assume atmospheric pressure is 1 bar and that the air is an ideal gas (Rg=0.287R_g = 0.287 kJ/(kg K)).

Formulas you may need
  • Ideal gas: pV=mRgTpV = mR_gT, so for a fixed mass p1V1T1=p2V2T2\dfrac{p_1V_1}{T_1} = \dfrac{p_2V_2}{T_2} (on the formula sheet)
  • Absolute pressure = gauge pressure + atmospheric pressure; temperatures in kelvin (learn this)
  1. (a)
    Determine the increase in pressure when the air temperature increases to 40 C.
  2. (b)
    Determine the mass of air that must be removed from the tyre to restore the gauge pressure to 2.4 bar at 40 C.