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The gauge pressure in your car tires is 2.50×105N/m2 at a temperature of 35.0°C when you drive it onto a ship in Los Angeles to be sent to Alaska. What is their gauge pressure on a night in Alaska when their temperature has dropped to −40.0°C ? Assume the tires have not gained or lost any air.

Respuesta :

Answer:[tex]1.644\times 10^{5} Pa[/tex]

Explanation:

Given

Initial Gauge Pressure [tex]P_i=2.50\times 10^5 N/m^2[/tex]

[tex]P_1_{abs}=(2.50+1.01325)\times 10^5[/tex]

Temperature [tex]T_i=35^{\circ}C\approx 308 K[/tex]

Final Temperature [tex]T_f=-40^{\circ}C\approx 233 K[/tex]

Also change in volume =0 i.e. [tex]\Delta V=0[/tex]

using [tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]

[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]

[tex]\frac{(2.50+1.01325)\times 10^5}{308}=\frac{P_f}{233}[/tex]

[tex]P_f=2.65\times 10^{5} Pa[/tex]

[tex]P_f_{gauge}=2.65-1.01325=1.644\times 10^{5} Pa[/tex]

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