Three liquids with masses m1, m2, m3 are thoroughly mixed. If their specific heats are c1, c2, c3 and …

Q: Three liquids with masses m1, m2, m3 are thoroughly mixed. If their specific heats are c1, c2, c3 and their temperatures T1, T2, T3, respectively, then the temperature of the mixture is

(a) $ \displaystyle \frac{c_1 T_1 +c_2 T_2 +c_3 T_3}{m_1 c_1 +m_2 c_2 +m_3 c_3} $

(b) $ \displaystyle \frac{m_1 c_1 T_1 + m_2 c_2 T_2 + m_3 c_3 T_3}{m_1 c_1 +m_2 c_2 +m_3 c_3} $

(c) $ \displaystyle \frac{m_1 c_1 T_1 + m_2 c_2 T_2 + m_3 c_3 T_3}{m_1 T_1 +m_2 T_2 +m_3 T_3} $

(d) $ \displaystyle \frac{m_1 T_1 +m_2 T_2 +m_3 T_3}{ c_1 T_1 + c_2 T_2 + c_3 T_3} $

Ans:(b)

Sol: Let T be the temperature of mixture , then

$ \displaystyle m_1 c_1 (T_1 – T) + m_2 c_2 (T_2 – T) + m_3 c_3 (T_3 – T) = 0$

$ \displaystyle m_1 c_1 T_1 + m_2 c_2 T_2 + m_3 c_3 T_3 = ( m_1 c_1 + m_2 c_2 + m_3 c_3 ) T $

$ \displaystyle T = \frac{m_1 c_1 T_1 + m_2 c_2 T_2 + m_3 c_3 T_3}{m_1 c_1 +m_2 c_2 +m_3 c_3} $