In: Physics

Two cylindrical iron rods both at temperatureThave lengthsLand 2L, and radiiRandR/2, respectively. If the rods’ temperatures are raised to 3T, and forces are appliedto prevent the rods from changing length, what is the ratio of the forces on the tworods?

**For 1st rod -**

Initial temperature = T

Final temperature = 3T

Change in Temperature, = 3T - T = 2T

Length = L

Radius of cross section = R

**For 2nd rod -**

Initial temperature = T

Final temperature = 3T

Change in Temperature, = 3T - T = 2T

Length = 2L

Radius of cross section = R/2

This problem will be solved by referring to modulus of elasticity of longitudinal objects i.e. Young's Modulus (Y)

We know that,

where, Stress = F/A i.e. Force F acting on area of cross section
A of the material to produce a deformation in the length of the
object. **Therefore, we can also say, that we have to apply
equal and opposite Force = F to prevent the rods from changing it's
length.** *( This is the Force F, we have to find in this
question )*

is the strain or deformity produced in the object of original length L

But, in this question, the strain or deformity in the object has originated from heating up of the object, therefore, thermal expansion has taken place, in which rod has linearly expanded from it's original shape.

This Thermal Expansion is given by :-

where is defined as strain as we have already discussed

is the coefficient of the linear thermal expansion

is the change in Temperature

**Now substituting eqn.(2) in eqn.(1) :-**

**Now, For 1st
rod :-**

**For 2nd rod
:-**

**Notice the Y
and are same for
both the rods, because these two quantities depend on the material
of which the object is made up of, and not on the dimensions of the
object. Since both the rods are made of Iron, they will have the
same value for both rods.**

**Therefore, eqn.(4) and (5) are equal. Equating them, we
get :-**

** ****(**
** and
cancel out )**

The two ends of an iron rod are maintained at different
temperatures. The amount of heat that flows through the rod by
conduction during a given time interval does not depend upon
A-the duration of the time interval.
B-the mass of the iron rod.
C-the length of the iron rod.
D-the thermal conductivity of iron.
E-the temperature difference between the ends of the rod.

Two infinitely long plates with surface temperatures maintained
at 600 K and 300 K
respectively are placed parallel to each other. Two infinitely long
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in the evacuated space between these plates. All the surfaces
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to elemental silicon.
SiO2(s) + 2 C(s) arrow sign Si(s) + CO(g)
Use the table to calculate the values of AH degrees, AS degrees,
and AG degrees for this reaction at 25 degrees C.
AH
(kJ mol-1 AG (kJ
mol-1) AS (J mol-1k-1)
SiO 2(s)
-910.7
856.3
41.5
C(s)
0
0
5.7
Si(s)
0
0
18.8
Co(g)
0
-137.2
197.6
Gibbs free energy for the reaction is_____________kJ

At high temperatures, coke reduces silica impurities in iron are
to elemental silicon.
SiO2(s) + 2 C(s) arrow sign Si(s) + CO(g)
Use the table to calculate the values of AH degrees, AS degrees,
and AG degrees for this reaction at 25 degrees C.
AH
(kJ mol-1 AG (kJ
mol-1) AS (J mol-1k-1)
SiO 2(s)
-910.7
856.3
41.5
C(s)
0
0
5.7
Si(s)
0
0
18.8
Co(g)
0
-137.2
197.6
Gibbs free energy for the reaction is_____________kJ

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2)
What is the moment of inertia of the disk about the axis of
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