Question

A 20-kg mass of iron at 100°C is brought into contact with 20 kg of aluminum at 200°C in an insulated enclosure. Determine the final equilibrium temperature of the combined system.

Option 1:
168°C

Option 2:
268°C

Option 3:
186°C

Option 4:
160°C​

Answer 1

Explanation:

186 degree Celsius will be the right answer for final equilibrium temp of the combined system

Answer 2

Given:

A 20-kg mass of iron at 100°C is brought into contact with 20 kg of aluminum at 200°C in an insulated enclosure.

To find:

The temperature at equilibrium ?

Calculation:

This is a question of CALORIMETRY .

Let the equilibrium temperature be $\theta$.

• Specific heat capacity of iron is 444.4 J/kg°C
• Specific heat capacity of aluminium is 900 J/kg°C

Now, applying equation of CALORIMETRY:

$\sf \therefore \: m1 \times c1 \times \Delta \theta_{1} = m2 \times c2 \times \Delta \theta_{2}$

$\sf \implies\:20 \times 444.4\times(\theta - 100) =20 \times 900 \times (200 - \theta)$

$\sf \implies\: 444.4\times(\theta - 100) = 900 \times (200 - \theta)$

$\sf \implies\: (\theta - 100) = 2.02 \times (200 - \theta)$

$\sf \implies\: \theta - 100= 405 - 2.02( \theta)$

$\sf \implies\: 3.02( \theta) = 505$

$\sf \implies\: \theta \approx {168}^{ \circ}$

So, temperature at equilibrium is approximately 168° C.