5th WEEK:THERMAL PROPERTIES OF MATTER

QUESTION 1

1. A sheet of copper has an area of 500cm³ at 0˚C. Find the area of this sheet at 80˚C.

ANSWER 1

1. The coefficient of area expansion is to good approximation 2α. Thus,
∆A = 2αA ∆t = 2(1.67 x 10ˉ⁵)(500)(80˚ - 0˚)
= 1.34cm²
The new area is 500 + 1.34 = 501.3cm²

QUESTION 2

2. Determine the change is volume of a block of iron 5 cm x 10 cm x 6 cm, when the temperature changes from 15˚C to 47˚C.

ANSWER 2

2. Vo = 300cm³ ; β=3α. Then,
∆V = 3α Vo∆T = 3(1.2 x 10ˉ⁵˚C⁻ ¹) (300cm³) (32˚C)
= 0.35 cm³

QUESTION 3

3. The coefficient of linear expansion of glass is found. If a bottle holds 50.000cm³ at 15˚C, what is its capacity at 25˚C?

ANSWER 3

3. The glass expands uniformly in all dimensions, so the capacity expands in proportion to the glass. The volume coefficient of expands to the linear coefficient by β = 3α. Then 3α. Then,
V = Vo (1+3α ∆T )
= (50.000cm³)[1+3(8.3 x 10ˉ⁶ ˚C⁻ ¹)(10˚C)]
V = 50.012 cm³.

QUESTION 4

4. Calculate the increase in volume of 100 cm³ of mercury when its temperature changes from 10 to 35˚C.

ANSWER 4

4. ∆V = β Vo∆T. The volume coefficient of expansion of mercury can be gotton.
β = 1.8 x 10ˉ⁴˚C⁻ ¹. Then,
∆V = (1.8 x 10ˉ⁴˚C⁻ ¹)(100cm³)(25˚C)
= 0.45 cm³.


QUESTION 5

5. Compute the increase in length of 50m of copper wire when its temperature changes from 12 to 32˚C?

ANSWER 5

5. ∆L = α Vo ∆T
= (1.67 x 10ˉ⁵˚C⁻ ¹)(50m)(20˚C)
= 16.7mm.