Need help related to heat, water and aluminium

[Sl1ver]

Homework Statement

I need help at identifying what forumala's to use to calculate the following

(Density of Aluminium 2770kg/m^3
An aluminium plate has a mass of 5kg and a surface area of 2m^2. The temperature of the plate is 450°C. The plate is immersed in a container of water of which the temperature rises from 20°C to 80°C. Only 70% of the heat energy given off by the plate is transferred to the water
Calculate
- Decrease in surface area of plate after being immersed in water
- percentage change in area due to temperature change
- heat transferred to water
- mass of the water

I have been going through the examples in the book and i just don't see how I will work it out. It seems I need a coefficient of linear expansion and coefficient of area expansion
but I just get 0 both times.

need to be pointed in the right direction to solve the problem as in formulas that would need to be used.

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Hi Sl1ver!

I have been going through the examples in the book and i just don't see how I will work it out. It seems I need a coefficient of linear expansion and coefficient of area expansion
but I just get 0 both times.

mmm

show us your full calculations, and then we'll see what went wrong, and we'll know how to help! ​

 

[Sl1ver]

coefficient of area = A1 -A2/A1(t2-t1)
=2m^2-2m^2/2m^2(80°C-20°)
=0/120
=0

and coefficient of linear expansion
using a as i can't find the proper symbol

2a = B
b=2/a
and then end up with zero as well.

so I can't see how zero and zero will help me

 

[tiny-tim]

It seems I need a coefficient of linear expansion and coefficient of area expansion

ah, yes …

i think you'll need to look those up in a table

 

[Nickie]

I would suggest using the following equations to help solve this problem:

1. Heat transfer equation: Q = mcΔT
This equation relates the heat transferred (Q) to the mass (m), specific heat capacity (c), and change in temperature (ΔT) of a substance.

2. Density equation: ρ = m/V
This equation relates the density (ρ) of a substance to its mass (m) and volume (V).

3. Coefficient of linear expansion equation: α = (ΔL/LΔT)
This equation relates the coefficient of linear expansion (α) to the change in length (ΔL), original length (L), and change in temperature (ΔT) of a substance.

4. Coefficient of area expansion equation: β = (ΔA/AΔT)
This equation relates the coefficient of area expansion (β) to the change in area (ΔA), original area (A), and change in temperature (ΔT) of a substance.

Using these equations, we can solve for the unknowns in the given problem:

1. Decrease in surface area of plate after being immersed in water:
To calculate the decrease in surface area, we can use the coefficient of area expansion equation. Since the plate is made of aluminium, we can use the coefficient of area expansion for aluminium, which is approximately 23.1 x 10^-6 /°C. We can also assume that the plate expands uniformly, so we can use the original surface area (2m^2) as the original area (A) in the equation. We also know the change in temperature (ΔT) of the plate, which is 450°C - 20°C = 430°C. Plugging in these values, we get:
β = (ΔA/AΔT) = (ΔA/2m^2)(23.1 x 10^-6 /°C)(430°C)
Solving for ΔA, we get:
ΔA = 2m^2(23.1 x 10^-6 /°C)(430°C) = 0.0199m^2
Therefore, the decrease in surface area is 0.0199m^2.

2. Percentage change in area due to temperature change:
To calculate the percentage change in area, we can use the following equation:
% change