Question

The coefficient of linear expansion of copper is 17 x 10^-6 K-1. A block of copper 30 cm wide, 45 cm long, and 10 cm thick is heated from 0°C to 100°C What is the change in the volume of the block?

Answer 1

The change in volume of a copper block when heated from 0°C to 100°C can be calculated using the coefficient of linear expansion for copper and the formula for volume expansion. The calculated change in volume is 688.5 cm³.

Step-by-step explanation:

The question is asking for the change in volume of a copper block due to thermal expansion upon heating. To calculate this change, we use the formula for volume expansion, which can be derived from the coefficient of linear expansion of the material. The coefficient of volume expansion (β) is equal to 3 times the coefficient of linear expansion (α).

Firstly, we identify α for copper, which is given as 17 x 10-6 K-1, and calculate β:

β = 3α = 3 x 17 x 10-6 K-1 = 51 x 10-6 K-1.

The initial volume (Vi) of the copper block is:

Vi = (width) x (length) x (thickness) = (0.30 m) x (0.45 m) x (0.10 m) = 0.0135 m3.

The temperature change (ΔT) is from 0°C to 100°C, so ΔT = 100°C.

We use the formula for volume expansion to find the change in volume (ΔV):

ΔV = βViΔT = 51 x 10-6 K-1 x 0.0135 m3 x 100°C.

ΔV = 0.0006885 m3 or 688.5 cm3.

The change in volume of the copper block when heated from 0°C to 100°C is 688.5 cm3.

Answer 2

The change in volume is
`6.885* 10^(- 5)\`

Solution:

As per the question:

Coefficient of linear expansion of Copper,
`\alpha = 17* 10^(- 6)\ K^(- 1)`

Initial Temperature, T =
`0^(\circ)` = 273 K

Final Temperature, T' =
`100^(\circ)` = 273 + 100 = 373 K

Now,

Initial Volume of the block, V =
`30* 45* 10* 10^(- 6)\ m^(3) = 0.0135\ m^(3)`

`V' = V(1 + \gamma \Delta T)`

`\gamma = 3\alpha`

`V' = V(1 + 3\alpha \Delta T)`

where

V' = Final volume

`V' - V= 0.0135* 17* 10^(- 6) * (T' - T))`

`\Delta V= 0.0135* 3* 17* 10^(- 6) * (373 - 273)) = 6.885* 10^(- 5)\`