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Answer :
When the temperature drops to 2.2 degrees Celsius, the tire pressure will decrease to approximately 202.1 kPa.
We can use the combined gas law which is derived from the ideal gas law. The combined gas law relates pressure, volume, and temperature without needing to know the quantity of gas, and is expressed as (P₁/T₁) = (P₂/T₂), where P₁ and T₁ are the initial pressure and temperature, and P₂ and T₂ are the final pressure and temperature.
To do so, we first convert temperatures to Kelvin by adding 273.15. Then we rearrange the formula to solve for P₂:
- P₂ = P₁ x (T₂/T₁)
- P₂ = 220 kPa x (275.35 K / 299.85 K)
- P₂ = 202.1 kPa
Therefore, the tire pressure will decrease to approximately 202.1 kPa.
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Answer:
202 KPa
Explanation:
Step 1:
Data obtained from the question.
Initial Pressure (P1) = 220 kPa
Initial temperature (T1) = 26.7°C
Final temperature (T2) = 2.2°C
Final pressure (P2) =?
Step 2:
Conversion of the Celsius temperature to Kelvin temperature.
Temperature (Kelvin) = temperature (celsius) + 273
T1 = 26.7°C + 273 = 299.7 K
T2 = 2.2°C = 2.2°C + 273 = 275.2 K
Step 3:
Determination of the new pressure.
The new pressure of the tire can be obtained as follow:
P1/T1 = P2/T2
220/299.7 = P2/275.2
Cross multiply to express in linear form
299.7 x P2 = 220 x 275.2
Divide both side by 299.7
P2 = (220 x 275.2)/299.7
P2 = 202 KPa
Therefore, the new pressure of the tire is 202 KPa
