Question

A 825 g iron block is heated to 352 degrees C and is placed in an insulated container (of negligible heat capacity) containing 40.0 g of water at 20.0 degrees C. What is the final equilibrium temperature of the water and iron? specific heat of water = 4186 J/(kg K), specific heat of water vapor = 2090 J/(kg K), specific heat of iron= 560 J/(kg K), latent heat of vaporization for water= 2.26*10^6 J/kg

Answer 1

Answer : The final equilibrium temperature of the water and iron is, 537.12 K

Explanation :

In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.

$q_1=-q_2$

$m_1\times c_1\times (T_f-T_1)=-m_2\times c_2\times (T_f-T_2)$

where,

$c_1$ = specific heat of iron =  560 J/(kg.K)

$c_1$ = specific heat of water = 4186 J/(kg.K)

$m_1$ = mass of iron = 825 g

$m_2$ = mass of water = 40 g

$T_f$ = final temperature of water and iron = ?

$T_1$ = initial temperature of iron = $352^oC=273+352=625K$

$T_2$ = initial temperature of water = $20^oC=273+20=293K$

Now put all the given values in the above formula, we get:

$(825\times 10^{-3}kg)\times 560J/(kg.K)\times (T_f-625K)=-(40\times 10^{-3}kg)\times 4186J/(kg.K)\times (T_f-293K)$

$T_f=537.12K$

Therefore, the final equilibrium temperature of the water and iron is, 537.12 K