Question

Three liquids with masses m1, m2, 3 are thoroughly
mixed. If their specific heats are ,C2,C3 and their
temperatures T1, T2, T3 respectively, then the temperature
of the mixture is
c;Ti + C₂T2 +CgTs
mic, mecz + macs
mc, Ti + mycąT, + m3c3T3
(
m₂ c + m₂ C2 + Mgcz
(c) mc, Ti + moc,T, + macgT;
m, Ti + m₂ T₂ + m₂ T3
m, Ti + m₂ T2 + mg T3
Ti + c ₂ Tz + c3T3
(6
)
(a
)​

Answer 1

$\\ \large\sf \: † \: \: \underbrace{\underline{Understanding \: concept :-} }$

Heat capacity (c')of a body is defined as the amount of heat energy required to raise its temperature by 1 K.

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: c' = \frac{Q}{ \triangle \: t}$

$\\ \large \underline{\bigstar \sf \: Required \: Question :-}$

Three liquids with Masses $\sf m_1 , m_2 , m_3$ are thoroughly mixed.If their specific heat are $\sf c_1 , c_2 , c_3$ and their temperatures are $\sf T_1 , T_2 , T_3$ respectively. Then the mixture is

$\\ \large \underline{\bigstar \sf \: \: Solution :-}$

Let the final temperature be 7°C,

Total heat supplied bye the three liquids in coming down to 0°C

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: \: m_1c_1T_1 + m_2c_2T_2 + m_3c_3T_3 \: - - - - - (1)$

The heat used by three liquids raising temperature from 0°C to T°C

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: \: m_1c_1T + m_2c_2T + m_3c_3T \: - - - - - (2)$

Now, By equating Equation (1) and (2) we get

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: \:( m_1c_1 + m_2c_2+ m_3c_3)T \:$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: \: = m_1c_1T_1 + m_2c_2T_2 + m_3c_3T_3 \:$

Therefore,

$\\ \\ \sf \: \: T = \frac{ m_1c_1T_1 + m_2c_2T_2 + m_3c_3T_3 \: }{m_1c_1 + m_2c_2+ m_3c_3}$

$\\ \large \underline{\bigstar \sf \: \: Note :-}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$Write question properly.