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1. A mountain biker goes for a ride in the desert. The air temperature is 21°C at the start of the ride, but the temperature in the desert will reach a peak of 51°C. The tires on the bike hold 15.6 L of nitrogen gas at a starting pressure of 249 kPa. The tires will burst when the internal pressure (Pb) reaches 269 kPa. Answer the following questions and show your work.
• How many moles of nitrogen gas are in each tire?
• What will the tire pressure be at the peak temperature in the desert?
• Will the tires burst at the peak temperature? Explain.
• To what pressure should the tire pressure be reduced before starting the ride to avoid bursting of the tires in the desert heat? (Assume no significant change in tire volume.)

Respuesta :

Edufirst
1) Data:

T₁ =  21°C

T₂ = 51°C.

V₁ = V₂ = 15.6 L

P₁ = 249 kPa.

Pb = 269 kPa.


Questions:


• n = ?
• P₂ = ?
• Will the tires burst at the peak temperature? Explain.
• To what pressure should the tire pressure be reduced before starting the ride to avoid bursting of the tires in the desert heat? (Assume no significant change in tire volume.)
Pi = ?


2) Formula:

PV = nRT
P₁ / T₁ = P₂ / T₂

3) Solution

i) n

P₁V₁ = nRT ⇒ n = P₁V₁ / [RT₁]

n = 249 kPa × 15.6 liter / [8.314 (liter-kPa / mol-K) × (21 + 273.15K) ] =

n = 1.588 mol

ii) P₂

P₂ = P₁ T₂ / T₁ = 249 kPa (50 + 273.15 K) / (21 + 273.15K) = 273.5 kPa


iii) Tires will burst, since P₂ > Pb

iv) Pi

Pi / T₁ = Pb / T₂

Pi = Pb T₁ / T₂ = 269 kPa (21 + 273.15K) / (50 + 273.15K) = 244.9 kPa

The pressure shoul to be reduced to less than 244.9 kPa before starting to avoid the  bursting of the tires in the desert heat.

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