An automobile tire is pumped up to a gauge pressure of 2.0 * 10⁵ Pa when the temperature is 27°C.What is its gauge pressure after the car has been running on a hot day so that the tire temperature is 77°C? Assume that the volume remains fixed and take atmospheric pressure to be 1.013 *10⁵ Pa. A)1.6 * 10⁵ Pa B)2.3 *10⁵ Pa C)2.5 * 10⁵ Pa D)3.6 * 10⁵ Pa E)8.6 * 10⁵ Pa

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The gauge pressure is given by:$$P_g = P - P_0$$where:* $$P_g$$ is the gauge pressure* $$P$$ is the absolute pressure* $$P_0$$ is the atmospheric pressureThe absolute pressure is given by:$$P = P_0 + P_g$$The volume of the tire is fixed, so the absolute pressure is proportional to the temperature. Therefore, we have:$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$where:* $$P_1$$ is the absolute pressure at temperature $$T_1$$* $$P_2$$ is the absolute pressure at temperature $$T_2$$Substituting the given values, we get:$$\frac{P_1}{273 K} = \frac{P_2}{350 K}$$Solving for $$P_2$$, we get:$$P_2 = \frac{350 K}{273 K} P_1$$Substituting the given values for $$P_1$$ and $$P_0$$, we get:$$P_2 = \frac{350 K}{273 K} (2.0 imes 10^5 Pa + 1.013 imes 10^5 Pa)$$$$P_2 = 2.5 imes 10^5 Pa$$Therefore, the gauge pressure is:$$P_g = P_2 - P_0 = 2.5 imes 10^5 Pa - 1.013 imes 10^5 Pa = 1.487 imes 10^5 Pa$$The closest answer choice is C) 2.5 F1F1F1S1*F1F1F10 10⁵ Pa.

An Automobile Tire Is Pumped Up to a Gauge Pressure