The temperatures of equal masses of three dif | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For equal masses $m$, the final temperature $T_{mix}$ of a mixture of two liquids with specific heats $C_1, C_2$ and initial temperatures $T_1, T_

Vedclass · Accepted Answer

$8: 10: 5$

Vedclass · Answer

(B) For equal masses $m$, the final temperature $T_{mix}$ of a mixture of two liquids with specific heats $C_1, C_2$ and initial temperatures $T_1, T_2$ is given by $T_{mix} = \frac{T_1 C_1 + T_2 C_2}{C_1 + C_2}$.For liquids $A$ and $B$:$20 = \frac{15 C_A + 24 C_B}{C_A + C_B} \Rightarrow 20 C_A + 20 C_B = 15 C_A + 24 C_B \Rightarrow 5 C_A = 4 C_B \Rightarrow C_A = \frac{4}{5} C_B$.For liquids $B$ and $C$:$26 = \frac{24 C_B + 30 C_C}{C_B + C_C} \Rightarrow 26 C_B + 26 C_C = 24 C_B + 30 C_C \Rightarrow 2 C_B = 4 C_C \Rightarrow C_B = 2 C_C$.Expressing all in terms of $C_C$:$C_B = 2 C_C$$C_A = \frac{4}{5} (2 C_C) = \frac{8}{5} C_C$Thus, $C_A : C_B : C_C = \frac{8}{5} C_C : 2 C_C : C_C = 8 : 10 : 5$.

$C_{1}$	$C_{2}$	$C_{3}$	$T$
$1 \ l$	$2 \ l$	$-$	$60^{\circ} C$
$-$	$1 \ l$	$2 \ l$	$30^{\circ} C$
$2 \ l$	$-$	$1 \ l$	$60^{\circ} C$
$1 \ l$	$1 \ l$	$1 \ l$	$\theta$

Similar Questions

$200 \,g$ of ice at $-20^{\circ} C$ is mixed with $500 \,g$ of water at $20^{\circ} C$ in an insulating vessel. The final mass of water in the vessel is ........... $g$ (specific heat of ice $= 0.5 \,cal \,g^{-1} {^{\circ}C}^{-1}$,latent heat of fusion of ice $= 80 \,cal \,g^{-1}$).

In a waterfall,the water falls from a height of $100 \ m$. If the entire kinetic energy $(K.E.)$ of the water is converted into heat,the rise in temperature of the water will be ........ $^\circ C$.

$50\, g$ of ice at $0^{\circ}C$ is mixed with $50\, g$ of water at $80^{\circ}C$. The final temperature of the mixture will be........ $^{\circ}C$.

$20 \, g$ of boiling water is poured into an ice-cold brass vessel (specific heat $0.1 \, cal/g-^{\circ}C$) of mass $100 \, g$. The resulting temperature is ........ $^{\circ}C$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module