Question

A bicycle tire with a volume of 0.00210 m^3 is filled to its recommended absolute pressure of 495 kPa on a cold winter day when the tire's temperature is -14°C. The cyclist then brings his bicycle into a hot laundry room at 32°C.

a. If the tire warms up while its volume remains constant, will the pressure increase be greater than, less than, or equal to the manufacturer's stated 10% overpressure limit?
b. Find the absolute pressure in the tire when it warms to 32 degrees Celcius at constant volume.

Answer 1

Answer:

Explanation:

.

Answer 2

(A) The pressure will be greater than 10% overpressure limit.

(B) The final pressure will be "582.915 kPa".

Given:

Volume,

• $V = 0.0021 \ m^3$

Initial pressure,

• $P_o= 495 \ kPa$

Initial temperature,

• $T_o = -14^{\circ} C$

            $= 259 \ K$

Final temperature,

• $T = 32^{\circ} C$

(B)

Number of moles,

→ $n = (\frac{P_o V}{RT_o} )$

then,

The final absolute pressure,

→ $P = \frac{nRT}{V}$

      $= (\frac{P_o V}{RT_o} )(\frac{RT}{V} )$

      $=(\frac{T}{T_o} )P_o$

      $= (\frac{305}{259} )\times 495$

      $= 582.915 \ kPa$

Thus the above approach is correct.

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