Question

Two liquid with masses $m_1=10\text{kg}$ and $m_2=20\text{kg}$ are thoroughly mixed. If there specific heats are $C_1=0.2{\text{cal/g -}}^{\circ }\text{C}$ and $C_2=0.1{\text{cal/g -}}^{\circ }\text{C}$ and their temperatures are ${30}^{\circ }\text{C}$ and ${40}^{\circ }\text{C}$ respectively, then the final temperature of the mixture is

• A. ${25}^{\circ }\text{C}$
• B. ${35}^{\circ }\text{C}$
• C. ${30}^{\circ }\text{C}$
• D. ${28}^{\circ }\text{C}$

Answer 1

The correct option is B ${35}^{\circ }\text{C}$

We know,
Temperature of mixture
$T_{\text{mix}}=\frac{m_1{C}_1{T}_1+m_2{C}_2{T}_2}{m_1{C}_1+m_2{C}_2}$

$=\frac{10\times 0.2\times 30+20\times 0.1\times 40}{10\times 0.2+20\times 0.1}$

$={35}^{\circ }\text{C}$