The menual of a car instructs the owner to inflate the tyres to pressure of 200 kPa. (a) What is the recommended gauge pressure ? (b) What is the recommended absolute pressure ? (c ) If after the required inflation of the tyres, the car is driven to a mountain peak. where the atmospheric pressrre is 10 % below that at sea level, what will be the tyre gauge read ? Atmospehric pressure ` =1.01 xx 10^5Pa.`

Options

A. 210 kPa
B. 220 kPa
C. 215 kPa
D. 230 kPa

Answer

B

Explanation

The manual gives the gauge pressure.
Thus reommended pressure `=P_g=220kPa`
Absolute pressure of air in tyres is (P)
=Atmospheric pressure (`P_a`)+Gauge pressure (`P_g)`
`=100+220=320kPa`
At the mountain, the atmospheric pressure is reduced by 10% i.e. it becomes 90 kPa=`P_a`
Since the absolute pressure of air in the tyre is not changed, then the gauge pressure (`P_s`)
`=P-P_a^'=320-90=230kPa`