Physics, 04.07.2019 17:00 tkdurocher

When the temperature of an automobile tire is 20°c, the pressure in the tire reads 32 psi on a tire gauge. (the gauge measures the difference between the pressures inside and outside the tire.) what is the pressure when the tire heats up to 40°c while driving? you may assume that the volume of the tire remains the same and that atmospheric pressure is a steady 14 psi.

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Answer from: adanamador8807

The initial pressure in the tire is given by the difference between the gauge pressure and the atmospheric pressure:

$p_1 = 32 PSI - 14 PSI = 18 PSI = 1.24 \cdot 10^5 Pa$

Let's also convert the initial and final temperature of the tire into Kelvin:

$T_1 = 20^{\circ}C=293 K$

$T_2 = 40^{\circ}C = 313 K$

We know that the volume of the tire remains the same, so we can use the fact that the ratio between pressure and temperature of the tire remains constant:

$\frac{P}{T}=constant$

which can be rewritten as

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

from which we can find the value of the final pressure, p2:

$P_2 = T_2 \frac{P_1}{T_1}=(313 K) \frac{1.24 \cdot 10^5 Pa}{293 K}=1.32 \cdot 10^5 Pa$

And converted back into PSI,

p_2 = 19.1 PSI

Answer from: Quest

the five characteristics of adolescence are biological growth and development, and undefined status, increased decision making, increased pressure and the search of self.

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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When the temperature of an automobile tire is 20°c, the pressure in the tire reads 32 psi on a tire...