posted by Alice on .
A granite column in a building is 8.50 m high and has a mass of 2.16 multiplied by 104 kg.
(a) How much heat (J) is needed to increase its temperature by 10.5°C, given its specific heat is 0.200 kcal/kg·°C?
(b) What is its change in length (m) if its coefficient of linear expansion is 2.50 multiplied by 10-6/°C?
(c) Calculate the force (N) it would exert if not allowed to expand, given its cross-sectional area to be 1.00 m2 and the Young's modulus for granite to be 45.0 multiplied by 109 N/m2. Note that this force is much larger than the weight it supports, so that it will expand almost freely.
(d) How much work (J) does it perform when it expands, if it supports a mass of 1.00 multiplied by 104 kg?
(e) What is its change in internal energy(J)?
m = ρV=837.36•
(a) Q=mcΔT=2.16•10⁴•837.36•10.5=1.9•10⁸ J
(b) α = 2.5•10⁻⁶ /℃
ΔL = α•L•ΔT = 2.5•10⁻⁶•8.5•10.5=2.23•10⁻⁴ m
(c) E= 45•10⁹ N/m²,
F/A = E•ΔL/L
F= A•E•ΔL/L =
W= m₀•g•ΔL =1•10⁴•9.8•2.23•10⁻⁴=21.85 J
(e) ΔU = W+Q = 21.85+ 1.9•10⁸ ≈1.9•10⁸ J