_{SPRING 2002 QUIZ 5}

PHYSICS 100A 

1. A structural steel I-beam is 15.0m long  when installed at 20.0°C. How much does its length change over the temperature extremes -30.0°C to 50.0°C?

Solution. 

 The increase in length when it is at 50.0°C will be

                           DL₁ = aL₀DT = [12 x 10^-6(C°)^-1](15.0m)(50.0°C - 20.0°C) = 5.4 x 10^-3m.

when the temperature decreases to -30.0°C, D>T  = -30.0°C - 20.0°C = -50.0°. Then

                           DL₂ = aL₀DT = [12 x 10^-6(C°)^-1](15.0m)(-50.0°) = -9 x 10^-3m.

So  the length change over the temperature extremes will be

                           DL = |DL₁| + |DL₂| 

                                 = 5.4 x 10^-3m + 9 x 10^-3m 

                                 =  1.44 x 10^-2m = 1.44cm.

2. If 5.00m³ of a gas initially at 40°C and under a pressure of 2.00atm is placed under a new pressure of 3.00atm, the temperature drops to 10°C; what is the volume of the gas?

Solution.           

For the two states of the gas we can write

                          P₁V₁ = nRT₁  and P₂V₂ = nRT₂, which can be combined to give

                          (P₂/P₁)(V₂/V₁) = T₂/T₁;