a) Suppose a meter stick made of steel and one made of invar (an alloy of iron a
ID: 2078656 • Letter: A
Question
a) Suppose a meter stick made of steel and one made of invar (an alloy of iron and nickel) are the same length at 0°C. What is their difference in length in millimeters at 52.0°C?
____mm
(b) Repeat the calculation for two 35.0 m long surveyor's tapes.
____mm
Question 2
Most automobiles have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. A radiator is made of copper and is filled to its 16.6 L capacity when at 13.5°C. What volume (in L) of radiator fluid will overflow when the radiator and fluid reach their 95.0°C operating temperature, given that the fluid's volume coefficient of expansion is = 400 106/°C? Note that this coefficient is approximate, because most car radiators have operating temperatures of greater than 95.0°C.
____L
Question 3
At a temperature of 20.70°C the hole in a steel plate has a diameter of 1.030 cm. If a steel rod with a diameter of 1.036 cm has to just slip through this hole, to what temperature should the plate be heated? The coefficient of area expansion of steel is
24 106/°C.
_____°C
PLEASE ANSWER ALL THE QUESTIONS DONT GIVE ANY WRONG ANSWERS THANKS FOR YOUR HELP !
Explanation / Answer
(A) L = L0 (1 + alpha deltaT)
deltaL = L0 delatT( alpha2 - alpha1)
for Steel, alpha1 = 13 x 10^-6
for invar, alpha2 = 1.3 x 10^-6
deltaL = (1 m ) (52 - 0) (13 - 1.3) x 10^-6
= 6.08 x 10^-4 m
= 0.608 mm
(b) when L0 = 35 m
deltaL = 0.0213 m Or 21.3 mm
---------------------------
2. deltaV = V0 beta deltaT
= (16.6 ) (400 x 10^-6) (95 - 13.5)
= 0.54 L
3. L = Lo (1 + alpha deltaT)
1.036 x 10^-2 = 1.030 x 10^-2 (1 + (24 x 10^-6)(T - 20.70))
6 x 10^-5 = 1.030 x 10^-2 x 24 x 10^-6 (T - 20.70)
T - 20.70 = 242.7
T = 263.4 deg C
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