college physic
posted by noah .
Determine a formula for the change in surface area of a uniform solid sphere of radius r if its coefficient of linear expansion is alpha A (assume constant) and its temperature is changed by Delta T.Assume the temperature chan ge is not large, Delta T^2 ~ 0.

college physics 
drwls
Area A = 4 pi R^2
lnA = ln(4 pi) + 2 ln R
dA/A = 2 dR/R = 2*(alpha)*dT
delta A = 2A*alpha*(delta T)
OR
A at T + deltaT
delta A = 4 pi (R + deltaR)^2  A
= 4 pi R(1 + alpha*deltaT)^2 A
= 4 pi R^2 *[1 + 2*alpha*deltaT +
(alpha*deltaT)^2]  A
= 2*A*alpha*deltaT + A*(alpha*deltaT)^2
(Ignore the second term in deltaT^2) 
college physic 
noah
TQ^^
Respond to this Question
Similar Questions

General chem lab
This involves Enthalpy of Neutralization: A student determined the calorimeter constant of the calorimeter. Using a plotted line. The student added 50ml of cold water to 50 ml of heated water in a Styrofoam cup. The initial temperature … 
physics!
The New River Gorge bridge in West Virginia is a steel arch bridge 518m in length. How much does the total length of the roadway decking change between temperature extremes of 20.0C and 35.0 C? 
AP Chemisty
N2(g)+3F2 yields 2Nf3(g) Delta H(degree)298=264KJ mol1;Delta S(degree)298=278J K1 mol1 The following questions relate to the synthesis reaction represented by the chemical equation above. a.)CAlculate the value of the standard … 
Physics
The average coefficient of volume expansion for carbon tetrachloride is 5.81 104 (°C)1. If a 43.0 gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0°C, how much will spill over when … 
Physics
In my lab of linear expansion, I need to find out the coefficient of linear expansion. The data I got for an aluminum rod are initial length is 59.7cm, the change in length is 95mm, the change in temperature is 75.4 Celsius degrees. … 
physics
NOTE: the formula for converting the CHANGE in temperature is NOT the same as simply converting the temperature! A bridge is made with segments of concrete 81 m long (at the original temperature). If the linear expansion coeﬃcient … 
physics
A uniform brass disk of radius R and mass M with a moment of inertia I about its cylindrical axis of symmetry is at a temperature T = 45 °C. Determine the fractional change in its moment of inertia if it is heated to a temperature … 
Physics
Two cylindrical rods are made of the same material and have the same length but one is hollow and other is solid. Both are heated to same increase in temperature. Which rod expands more? 
Physics
I'm also stumped by this one: 3. A bimetallic strip (117 cm by 1 cm by 0.01cm) has aluminum (a = 23x10^6 1/Celsius) on one side and has steel (a= 12x10^6 1/Celsius) on the other. It is perfectly straight at room temperature (20 celsius). … 
Calculus Homework
You are blowing air into a spherical balloon at a rate of 7 cubic inches per second. The goal of this problem is to answer the following question: What is the rate of change of the surface area of the balloon at time t= 1 second, given …