The pressure of air in an automobile tire at a temperature of 27°C is 1.75 bar (gauge). Due to running, the temperature of the air in the tire rises to 87°C. What will be the gauge pressure during this running? [ $P_{a t m} = 1.01$ bar, volume of tire is assumed constant]

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SJVN ET Mechanical 2019 Official Paper

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Answer 1

Concept:

For constant volume: $ \frac{P_1}{T_1} = \frac{P_2}{T_2} \Rightarrow P_2 = P_1 \cdot \frac{T_2}{T_1} $

Calculation:

Given:

$ P_1^{gauge} = 1.75 \, \text{bar} $, so $ P_1^{abs} = 1.75 + 1.01 = 2.76 \, \text{bar} $
$ T_1 = 27^\circ C = 300 \, \text{K}, ~T_2 = 87^\circ C = 360 \, \text{K} $

$ P_2^{abs} = 2.76 \cdot \frac{360}{300} = 3.312 \, \text{bar} $

$ P_2^{gauge} = 3.312 - 1.01 = {2.302 \, \text{bar}} $