It will take 7.777 minutes for the tire to reach the original pressure of 35.0 psi .
Given ,
A truck tire has a volume of 218L and is filled with air to 35.0psi at 295K .
After a drive , the air heats up to 318K .
a) Given , volume is constant .
P1 = 35 psi , T1 =295K , T2 = 318K , P2 = ?
We know , ideal gas equation ,
PV= nRT
=> P1/T1= P2/T2
=> P2 = P1 *T2/T1 =35 *(318) / 295 = 37 psi
b) the volume increased by 2% .
2% of 218 = 4.36
V2 = 222.36 L
P1 *V1=P2*V2
=> P2 = P1*V1/V2 = 35*(218)/ 222.36 = 34.313 psi
c) Given , the temperature is constant ,
thus , P1/n1 = P2/n2
=> n1/n2 = P1/P2 = 35/34.313 = 1.02
=> n1 = 1.02 n2
At the initial condition ,
PV = nRT
n1 = P1 V1 / R T1
= 241316.495 pa * (218 L ) / 295K *( 8.314 *10^3 pa L K^-1 mol^-1)
= 52606.9959/2452.63 = 21.449 mol
n2 = 21.02 mol
n= n1-n2 = 0.42 mol
given , the mass of air is 28.8g .
thus 1.5g of gas contains = 0.054 mol
thus , 0.054 mol gas lose in 1 minutes
0.42 mol of gas lose in = 0.42/0.054 = 7.777 minutes
Hence , it will take for the tire to reach the original pressure of 35.0 psi is 7.777 minutes .
Learn more about ideal gas equation here:
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Disclaimer : incomplete question . here is the complete question .
Question : A truck tire has a volume of 218 L and is filled with air to 35.0 psi at 295K . after a drive , the air heats up to 318 K .(a) if the tire volume is constant , what is the pressure? (b) if the volume increases 2.0% , what is the pressure ? (c) if the tire leaks 1.5g of air per minutes and the temperature is constant , how many minutes will it take for the tire to reach the original pressure of 35.0 psi ( M of air = 28.8g/mol) ?
