A liquid of mass M and specific heat S is at a temperature 2t. If another liquid of mass M and thermal capacity 1.5 times, at a temperature of (t/3) is added to it, the resultant temperature will be :

Question

A liquid of mass M and specific heat S is at a temperature 2t. If another liquid of mass M and thermal capacity 1.5 times, at a temperature of (t/3) is added to it, the resultant temperature will be : (A) (4/3)t (B) t (C) (t/2) (D) (2/3)t

Tardigrade Admin · Accepted Answer

Let the common temperature of the mixture be

T

.
For first liquid, mass,

M

, specific heat of liquid,

S

and initial temperature of liquid,

2 t

.
For second liquid, mass,

M

, specific heat of liquid,

1.5 S

and initial temperature of liquid,

\frac{t}{3}

Heat loss by the hot liquid

=

Heat consumed by cold liquid

MS (2 t - T) = M (1.5 S) (T - \frac{t}{3}) \Rightarrow 2 t - T = 1.5 T - \frac{t}{2} \Rightarrow \frac{5}{2} T = \frac{5}{2} t

\Rightarrow T = t

Q. A liquid of mass $M$ and specific heat $S$ is at a temperature $2 t .$ If another liquid of mass $M$ and thermal capacity $1.5$ times, at a temperature of $\frac{t}{3}$ is added to it, the resultant temperature will be :

$\frac{4}{3} t$

$t$

$\frac{t}{2}$

$\frac{2}{3} t$

Q. A liquid of mass M and specific heat S is at a temperature 2t. If another liquid of mass M and thermal capacity 1.5 times, at a temperature of 3t​ is added to it, the resultant temperature will be :

34​t

t

2t​

32​t

Q. A liquid of mass $M$ and specific heat $S$ is at a temperature $2 t .$ If another liquid of mass $M$ and thermal capacity $1.5$ times, at a temperature of $\frac{t}{3}$ is added to it, the resultant temperature will be :

$\frac{4}{3} t$

$t$

$\frac{t}{2}$

$\frac{2}{3} t$