A car tire contains 0.0320 m3 of air at a pressure of 2.35 ✕ 105 N/m2 (about 34 psi). How much more internal energy (in J) does this gas have than the same volume has at zero gauge pressure (which is equivalent to normal atmospheric pressure) ? (Assume the tire pressure of 2.35 ✕ 105 N/m2 is absolute pressure, not gauge pressure. Assume for this question that air is monatomic.)

Question

Lion

Physics

7 February, 23:24

A car tire contains 0.0320 m3 of air at a pressure of 2.35 ✕ 105 N/m2 (about 34 psi). How much more internal energy (in J) does this gas have than the same volume has at zero gauge pressure (which is equivalent to normal atmospheric pressure) ? (Assume the tire pressure of 2.35 ✕ 105 N/m2 is absolute pressure, not gauge pressure. Assume for this question that air is monatomic.)

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Blossom · Answer 1

The internal energy in the system is

ΔE = 1.072 x 10 ⁴ J

Explanation:

Given

V = 0.0320 m³

P₁ = 2.35 x 10 ⁵ Pa

P₂ = 1.01 x 10 ⁵ Pa

To determine the internal energy

ΔE = ⁵/₂ * V * (P₂ - P₁)

ΔE = ⁵/₂ * 0.0320 m³ * (2.35 x 10 ⁵ - 1.01 x 10 ⁵) Pa

ΔE = ⁵/₂ * 0.0320 m³ * (134 kPa)

ΔE = 10720 J

ΔE = 1.072 x 10 ⁴ J