# 4. Suppose your bicycle tire is fully inflated, with an absolute pressure of 7.00 x 10°...

4. Suppose your bicycle tire is fully inflated, with an absolute pressure of 7.00 x 10° Pa at a temperature of 18.0 °C. What is the pressure after its temperature has risen to 35.0 °C? Assume that there are no appreciable leaks or changes in volume. PE 5. A high vacuum system used in physics experiments can achieve a pressure as low as 1.0 x 10-10 N/m² at 20 °C. Estimate the number of molecules in a cubic millimeter (V = 1.0 mm3) at this pressure and temperature? (PV = NkgT and kb = 1.38 x 10-23 J/K) N =

SOLUTION :

4.

P/T = constant for the given volume.

=> P1/T1 = P2/T2

=> P2 = P1 (T2/T1) = 7 * 10^5 ((273+35) / (273+18))

=> P2 = 740893.47  Pa

So, pressure at 35ºC will be 740893.47 Pa (ANSWER).

5.

PV = N Kb T

=> 1*10^(-10) * 1.0 * 10^(-9)  = N * 1.38*10^(-23) * (273+20)

=> 1 * 10^(-19) = 4.0434*10^(-21) * N

=> N =  1 * 10^(-19) / (4.0434 * 10^(-21)) = 24.73 molecules

So, 24.73 molecules are there in 1 cubic mm volume. (ANSWER).

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