Question

An automobile tire has a volume of 988 in^3 and contains air at a gauge pressure of 24 lb/in^2(psi) when the temperature is -2.6 ℃. Find the temperature of air in the tire when its volume increases to 1020 in^3 and its gauge pressure becomes 26.9 lb/in^2.

Answer 1

Answer on Question #72386-Physics-Other

An automobile tire has a volume of 988 in^3 and contains air at a gauge pressure of 24 lb/in^2(psi) when the temperature is -2.6 °C. Find the temperature of air in the tire when its volume increases to 1020 in^3 and its gauge pressure becomes 26.9 lb/in^2.

Solution

For the ideal gas we have:

$$\frac {p _ {1} V _ {1}}{T _ {1}} = \frac {p _ {2} V _ {2}}{T _ {2}}$$ $$T _ {2} = T _ {1} \left(\frac {p _ {2}}{p _ {1}}\right) \left(\frac {V _ {2}}{V _ {1}}\right)$$ $$T _ {2} = (273.15 - 2.6) \left(\frac {26.9}{24}\right) \left(\frac {1020}{988}\right) = 313.06\,K.$$

The temperature of air in the tire when its volume increases to 1020 in^3 and its gauge pressure becomes 26.9 lb/in^2 is

$$t _ {2} = 313.06 - 273.15 = 39.9\,{}^{\circ}\text{C}$$

Answer: 39.9°C.

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