4) A granite column in a building is 9.00 m high and has a mass of 2.16 10 4 kg.

Question

4) A granite column in a building is 9.00 m high and has a mass of 2.16 104 kg.(a) How much heat is needed to increase its temperature by 10.5°C, given its specific heat is 0.200 kcal/kg·°C?
J
(b) What is its change in length if its coefficient of linear expansion is 2.50 10-6/°C?
m
(c) Calculate the force 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 45.0 109 N/m2. Note that this force is much larger than the weight it supports, so that it will expand almost freely.
N
(d) How much work does it perform when it expands, if it supports a mass of 1.00 104 kg?
J
(e) What is its change in internal energy?
J
(f) What is the source of energy for the work performed?

5) A hand-driven tire pump has a 3.00 cm diameter piston and a maximum stroke of 31.0 cm.

(a) How much work do you do in one stroke if the average gauge pressure is 2.40 105 N/m2 (about 35 psi)? (You may consider this an isothermal process.)
J
(b) What average force do you exert on the piston, neglecting friction and gravity?
N

Explanation / Answer

4) Given,

Height of column, h = 9 m

Mass, m = 2.16 x 104 kg

Change in temperature, T = 10° C

Specific heat constant, Cp = 0.200 kcal/kg °C = 837.36 J/kg

(a) Q = m Cp T = 2.16 x 104 x 837.36 x 10.5 = 1.9 x 108 J

(b) Coefficient of linear expansion, = 2.5 10-6 /

Change in length, L = L T = 2.5 x 10-6 x 9 x 10.5 = 2.36 x 10-4 m

According to chegg guidelines I can answer one question at a time, so please post other questions seperately. Please rate my answer if you find it helpful, good luck...

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