An automobile tire has a volume of 0.0150 m3 on a cold day when the temperature of the air in the tire is 5.0o C and atmospheric pressure is 1.02 atm. Under these conditions the gauge pressure is measured to be 1.70 atm (about 25 lb/in.2). After the car is driven on the highway for 30 min, the temperature of the air in the tires has risen to 45.0o C and the volume has risen to 0.0159 m3. What then is the gauge pressure?

Solution 61P Step 1: Here V = 0.0150 m 3 1 T = 5 C = 278 K 1 The atmospheric pressure, P out= 1.02 atm The gauge pressure, P = 1.70 atm. gauge We know that, the inside pressure of the tyre is, P = P + P = 1.02 + 1.70 = 2.72 atm. in gauge out Step 2: After the car is driven, the volume, temperature and pressure reached to, 3 V 2 0.0159 m . T = 45 C = 318 K . 2 The inside pressure we have to find first. The equation says that, P1V 1 P2V 2 T = T ---------------------(1) 1 2 2.72×0.0150 P2×0.0159 278 = 318 2.72×0.0150 318 P = 2 278 × 0.0159 = 2.935 atm This is the pressure inside the tyre after 30 minutes.