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Rashid [163]
3 years ago
13

The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pres

sure gage reads 210 kPa. If the volume of the tire is 0.025 m3, determine the pressure rise in the tire when the air temperature in the tire rises to 44°C. Also, determine the amount of air that must be bled off to restore pressure to its original value at this temperature. Assume the atmospheric pressure to be 100 kPa.
Engineering
1 answer:
kirza4 [7]3 years ago
4 0

Answer:

ΔP=19.76 KPa

\Delta m=10^{-3}\ gm

Explanation:

Given that

T_1= 25C,  P_1= 210 \KPa \gauge

atmospheric pressure = 100 kPa.

So absolute pressure = Atmospheric pressure + gauge pressure

P_1=210+100\ KPa (absolute)

P_1=310\ KPa (absolute)

Here volume of air is constant .We know that for constant volume pressure

\dfrac{P_1}{T_1}=\dfrac{P_2}{T_2}

here

T_2= 44C

T_1=273+25=298K

T_2=273+44=317K

\dfrac{P_1}{T_1}=\dfrac{P_2}{T_2}

\dfrac{310}{298}=\dfrac{P_2}{317}

P_2=329.76\ KPa (absolute)

So rise in pressure

\Delta P=P_1-P_2

ΔP=329.76-310 KPa

ΔP=19.76 KPa

m_1=\dfrac{P_1V}{RT_1}

m_1=\dfrac{310\times 0.025}{0.287\times 298}

m_1=0.090615\ kg

m_2=\dfrac{P_2V}{RT_2}

m_2=\dfrac{329.76\times 0.025}{0.287\times 317}

m_2=0.090614\ kg

Δm=0.090615 - 0.090614 kg

\Delta m=10^{-3}\ gm

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