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## Homework Statement

I need to find the temperature of the air in a sealed box after 15minutes, that has been cooled by a Peltier device. The set up is as follows:

The peltier device is between 2 aluminium blocks of the same Area but depth of 1cm. The aluminium block that is receiving heat from the peltier device is connected to a heat sink. The other aluminium block is connected to a larger aluminium block that is inside the cool box (there is a hole big enough for them to be in contact). The larger block blocks off the hole and has the same depth as the other blocks. A heat sink is also attached to larger aluminium block.

The thermal conductivity of: aluminium is 237 W m^-1 K^-1, heat sink 201 W m^-1 K^-1. Area of peltier is 16 cm^2

Depth of heat sink is 7cm

Area of heat sink is 64cm^2

The temperature of the pelter device (cool side) stays about constant at 279K for 15 minutes (after 15 minutes its 281K)

## Homework Equations

ΔQ/Δt = k A (T_{hot} - T_{cold})/depth

## The Attempt at a Solution

So far I have assumed that T_hot is just room temperature in this case let that be (301K).

I have also assumed that each object starts at room temperature

so for going from the peltier device to the small aluminium block:

ΔQ1/Δt=237*(1.6*10^-3)*(301-279)/0.01=834.24

but for the small aluminium block to the larger one:

ΔQ2/Δt=237*(1.6*10^-3)*(301-T_small block)/0.01

Then heat sink ΔQ2/Δt=201*(6.4*10^-3)*(301-T_large block)/0.07

but I have no idea how to find T_s,b and T_l,b and how I can use this to find the temperature of the air in the box