The pressure of an automobile tire is measured to be 190 kPa( gage ) before a trip and 215 kPa(

step 1 Here you have to write the known first. So atmospheric pressure equals 95 kilo -pascal. P -1 is

The pressure of an automobile tire is measured to be 190...

The pressure of an automobile tire is measured to be $190 \mathrm{kPa}(\text { gage })$ before a trip and $215 \mathrm{kPa}(\text { gage })$ after the trip at a location where the atmospheric pressure is 95 kPa. If the temperature of air in the tire before the trip is $25^{\circ} \mathrm{C},$ the air temperature after the trip is $(a) 51.1^{\circ} \mathrm{C}$ (b) $64.2^{\circ} \mathrm{C}$ $(c) 27.2^{\circ} \mathrm{C}$ $(d) 28.3^{\circ} \mathrm{C}$ $(e) 25.0^{\circ} \mathrm{C}$

The pressure of an automobile tire is measured to be $190 \mathrm{kPa}(\text { gage })$ before a trip and $215 \mathrm{kPa}(\text { gage })$ after the trip at a location where the atmospheric pressure is 95 kPa. If the temperature of air in the tire before the trip is $25^{\circ} \mathrm{C},$ the air temperature after the trip is
$(a) 51.1^{\circ} \mathrm{C}$
(b) $64.2^{\circ} \mathrm{C}$
$(c) 27.2^{\circ} \mathrm{C}$
$(d) 28.3^{\circ} \mathrm{C}$
$(e) 25.0^{\circ} \mathrm{C}$

Key Concepts

Constant Volume Process

In a system where the volume remains constant, the ideal gas law simplifies the relationship between pressure and temperature to P/T = constant. This means that any change in absolute pressure directly reflects a proportional change in absolute temperature, making it a key concept in analyzing heat effects in confined gases.

Ideal Gas Law

The ideal gas law (PV = nRT) relates the pressure, volume, temperature, and amount of gas. It is fundamental in understanding the behavior of gases under various conditions. In problems where the volume and number of moles of gas remain constant, the law specifically shows that pressure and temperature are directly proportional, forming the basis for many thermodynamic calculations.

Gauge vs Absolute Pressure

Gauge pressure measures the pressure relative to the surrounding atmospheric pressure, whereas absolute pressure is the total pressure including the atmospheric contribution. In thermodynamic problems, absolute pressures are required for correctly applying gas laws, since these laws are based on absolute quantities.

Temperature Conversion

When applying the ideal gas law, temperatures must be converted to the Kelvin scale, which is an absolute temperature scale. This conversion ensures accurate calculation since the proportionality between pressure and temperature holds true only when the temperature is measured from absolute zero.

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