For mercury to expand from 4.0 cm^3 to 4.1 cm^3, what change in temperature is necessary?
Mercury has a volume expansion coefficient of 180x10^-6/C degrees.
A) 400 degreeC
B) 139 degreeC
C) 14 degreeC
D) 8.2 degreeC
The answer is B.
Here is how to derive the answer. The formula for thermal expansion of volume is
Change in volume = gamma*original volume*change in temperature where gamma is the volume expansion coefficient.
Since we have been given the change in volume, the original volume, and the coefficient, this becomes an algebra problem. The equation is
.1 = 180E-6*4*(change in temp)
We multiply the coefficient and the original volume, which gets us 7.2E-4. We divide both sides by that and get the answer which is
change in temp = 139
The extent of expansion in volume due to increase in temperature ids given by the formula:
v2 - v1 = v1*(t2 - t1)*E
v1 = initial volume = 4 cm^3 (Given)
v2 = Final volume = 4.1 cm^3 (Given)
t1 = Initial temperature
t2 = Final temperature
E = Volume expansion coefficient = 180*10^(-6)/degree C (Given)
Substituting these values in the above equation we get:
4.1 - 4 = 4*(t2 - t1)*[180*10^(-6)
Therefore: 0.1 = (t2 - t1)*[72*10^(-5)]
Therefore: t2 - t1 = 0.1/[72*10^(-5)] =138.88 degrees C
Rounding this off to nearest whole number:
t2 - t1 = 139 degrees C
Therefore change in temperature necessary for expansion is 139 degrees C.
Thus the option B) is correct.