A brass rod is 40.1 cm long and an aluminum rod is 79.3 cm long when both rods a
ID: 1682765 • Letter: A
Question
A brass rod is 40.1 cm long and an aluminum rod is 79.3 cm long when both rods are at an initial temperature of 0 degrees celsius. The rods are placed in line with a gap of 0.6 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. In Fig. 17.1a, the temperature at which contact of the rods barely occurs, in degrees celsius, is closest to: a)200 b)244 c)233 d)222 e)211
A brass rod is 40.1 cm long and an aluminum rod is 79.3 cm long when both rods are at an initial temperature of 0 degrees celsius. The rods are placed in line with a gap of 0.6 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. In Fig. 17.1a, the temperature at which contact of the rods barely occurs, in degrees celsius, is closest to: a)200 b)244 c)233 d)222 e)211
Explanation / Answer
Brass Rod + Aluminum Rod L = L0_1*(1+a_1*delT) + L0_2*(1+a_2*delT) = 120 L0_1 = 40.1 cm L0_2 = 79.3 cm a_1 = 2e-5 a_2= 2.4e-5 (L - L0_1 - L0_2) = L0_1*a_1*delT + L0_2*a_2*delT delT = (L-L0_1-L0_2)/(L0_1*a_1 + L0_2*a_2) delT = (120 - 40.1 - 79.3) /(40.1*2e-5+79.3*2.4e-5) delT = 221.795061 C ~ 222C Answer is D)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.