1)A concrete highway is built of slabs 16.0 m long (at 18 °C). How wide should t

Question

1)A concrete highway is built of slabs 16.0 m long (at 18 °C). How wide should the expansion cracks be (at 18 °C) between the slabs to prevent buckling if the annual extreme temperatures are 27 °C and 54 °C?(the coefficient of linear expansion of concrete is 1.20 × 10-5 °C-1)

2)A quartz sphere is 14.0 cm in diameter. What will be its change in volume if its temperature is increased by 320 °F? (the coefficient of volume expansion of quartz is 1.50 × 10-6 °C-1)

3)A small immersion heater is rated at 360 Watts. Estimate how long it will take to heat a cup of soup (assume this is 230g of water) from 21 °C to 52 °C.

Explanation / Answer

dL = aLodT

Lo = 16m

dT = (54-18) ; a = 1.20 x 10^-5

dL = 1.20 x 10^-5 x 16 x (54-18)

dL = 6.912 x 10^-3 m = 6.912 mm

The space between the slabs must be the same as the expansion of the the slabs.so answer is 6.912 mm

part b )

volumetric expansion = dV = g*Vo*dT

here ,

g = volumetric expansion cofficient = 1.50 x 10^-6

Vo = 4/3*pi*r^3 ; r = 7cm = 7 x 10^-2 m

dT = 320

dV = g*Vo*dT

dV = 1.5 x 10^-6 x 4/3 x pi * (0.07)^3 x 320

dV = 6.89 x 10^-7 m^3

dV = 6.89 x 10^-7 m^3 * 1 x 10^6 = 0.689 cm^3

part c)

dQ = mcdT

dQ = heat = power * t

m = weight ; c = specific heat ; dT = temprature difference

(360)*t = 0.230 * 4186 * 31

t = 82.91 s = 1.38 min

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