Question

a 150 g sample of water (initially at 45 C) is mixed with an unknown mass of water (initially at 84 C). the final temperature of the system is 67.3 C. Determine the mass of water

Answer 1

Answer : The unknown mass of water is, 200.3 grams.

Explanation :

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

$q_1=-q_2$

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

As,

$c_1=c_2$ = specific heat water

So,

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

where,

$m_1$ = mass of water = 150 g

$m_2$ = mass of unknown water  = ?

$T_f$ = final temperature of mixture = $67.3^oC$

$T_1$ = initial temperature of water = $45^oC$

$T_2$ = initial temperature of unknown water = $84^oC$

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

$150g\times (67.3-45)^oC=-m_2\times (67.3-84)^oC$

$m_2=200.3g$

Therefore, the unknown mass of water is, 200.3 grams.