Question

An automobile tire at 30°C has a pressure of 3. 00 atm. Temperature decreases to -5°C. Assume that there is no volume change in the tire. How does the tire pressure change in response to the temperature change?.

Answer 1

The gas in the tire has been assumed to be an ideal gas. The relationship between pressure and temperature at constant volume has been given as:

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

Computation for relationship between Pressure and Temperature

The initial pressure of tire has been, $P_1=3\;\rm atm$

The initial temperature has been, $T_1=x$

The final temperature has been, $T_2=-5$

Substituting the values for the final pressure, $P_2$

$\dfrac{3}{x} =\dfrac{P_2}{-5}\\\\ P_2x=-15$

The product of initial temperature and final pressure of the gas been -15.

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