a brass rod is 54.2 cm long and an aluminum rod is 64.7 cm long when both rods a

Question

a brass rod is 54.2 cm long and an aluminum rod is 64.7 cm long when both rods are at an initial temperature of 0 deg C. The rods are placed in line with a gap of 1.1 cm between them. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature is raised until the two rods are barely in contact. The coefficients of linear expansion of brass and aluminum are 2.0 x 10^-5 K^-1 and 2.4 x 10^-5 K^-1 respectively. The temperature at which contact of the rods barely occurs, in deg Celcius, is closest to:

Explanation / Answer

The change in the linear dimension can be estimated to be:L/L=T

where is coefficients of linear expansion

in this question one end is held fixed so they can expand in gap only

therefore L(brass)+L(aluminum)=1.1 cm

54.2*2*10^-5*(T-0)+64.7*2.4*10^-5*(T-0)=1.1

solving this we get T=417.17 deg C

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