Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
A tractor tyre contains 31 L of air at a pressure of 190 kPa and a temperature of 30°C. Using R=8.314 J (gmol)⁻¹ K⁻¹ and molecular mass of air = 29 g (gmol)⁻¹, the mass of air contained in the tyre is M × 10⁻³ kg. The value of M is________.
Official Answer Key:
66.7 to 67.9
Step-by-Step Solution & Explanation
Ideal gas law: PV = nRT, with P = 190,000 Pa, V = 0.031 m³, T = 303.15 K.
n = PV/RT = (190,000 × 0.031)/(8.314 × 303.15) = 5890 / 2520.0 = 2.3373 mol.
mass = n × M_air = 2.3373 × 29 = 67.78 g = 67.78 × 10⁻³ kg ⇒ M ≈ 67.8.
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