Question

An automobile tire has a maximum rating of 38.0 psi (gauge pressure). 

Part A 

The tire is inflated (while cold) to a volume of 11.8 L and a gauge pressure of 36.0 psi 

(Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is 14.7 psi.) at a temperature of 12.0°C. While driving on a hot day, the tire warms to 65.0°C and its volume expands to 12.2 L. 

What is the total pressure (gauge pressure + atmospheric pressure) in the tire after warming on a hot day? 

Answer 1

Following is the - complete Answer -&- Explanation: for the given Question: in....typed format...

Answer:

Total pressure in the tire, after warming of the day = 3.81 atm (atmosphere)

Explanation

Following is the complete Explanation, for the above Answer.

• Given:

1. Initial volume, of the tire = 11.8 L  ( liters ) , on a cold day....
2. Gauge pressure on the cold day : p₁ = 36.0 psi = 2.449 atm ,( since: 1.0 psi = 0.068 atm )
3. Temperature of the tire: on cold day = 12.0 ^oC = ( 12.0 + 273.15 ) = 285.15 K ( kelvin )
4. Gauge pressure = Total pressure - Atmospheric pressure
5. OR, total pressure = gauge pressure + atmospheric pressure
6. assuming: Atmospheric pressure, remains constant , at any temperature ...
7. Atmospheric pressure =  14.7 psi = 1.0 atm
8. Volume of the tire: on a Hot day =  12.2 L ( liters )
9. Temperature of the tire, on a Hot day =  65.0 ^oC = ( 65.0 + 273.15 ) = 338.15 K ( kelvin )
10. Let, gauge pressure: on the hot day = p₂  ( atm )

• ​​​​​​​Step - 1:

​​​​​​​Assuming the value of the atmospheric pressure, to remain constant, we would get the following:

We know, the general gas equation:  

i.e. P₁ x V₁ / T₁ = P₂ x V₂ / T₂   -------------------------------------Equation - 1

Where:

1. P₁= initial gauge pressure ( cold day ) =  2.449 atm ( atmospheric pressure )
2. V₁ =  volume on a cold day = 11.8 L
3. T₁ =  Temperature on a cold day = 285.15 K ( kelvin )
4. P₂ = gauge pressure on hot day = ( unknown )
5. V₂ =  volume of the tire , on a hot day = 12.2 L
6. T₂ = temperature, on the hot day = 338.15 K ( kelvin )

• ​​​​​​​Step - 2:

​​​​​​​Plugging in values, in the given: Equation - 1, we would get:

P₁ x V₁ / T₁ = P₂ x V₂ / T₂   -------------------------------------Equation - 1

[( 2.449 atm ) x ( 11.8 L )] / ( 285.15 K ) = [ (P₂) x ( 12.2 L ) ]  / ( 338.15 K )

P₂ = { ( 2.449 atm ) x ( 11.8 L )] / ( 285.15 K ) } x (338.15 K ) / ( 12.2 L ) = 2.81 atm.

Therefore, we get gauge pressure : on Hot day :   P₂ = 2.81 atm

• Step - 3:

​​​​​​​Thus, applying the given formula: we get :

Total pressure =  gauge pressure + atmospheric pressure = 2.81 atm + 1.0 atm = 3.81 atm  

• Answer:

​​​​​​​Total pressure, on a hot day = 3.81 atm ( Answer )