JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Heat & Thermodynamics

The temperature of equal masses of three different liquids

x, y

and

z

are

1 0^{\circ} C, 2 0^{\circ} C

and

3 0^{\circ} C

respectively. The temperature of mixture when x is mixed with y is

1 6^{\circ} C

and that when y is mixed with z is

2 6^{\circ} C

. The temperature of mixture when x and z are mixed will be:

Answer: (B)

Solution

The masses are equal, so only the specific heats enter. Mixing

x

with

y

c_{x} (16 - 10) = c_{y} (20 - 16) \Rightarrow 3 c_{x} = 2 c_{y}

Mixing

y

with

z

c_{y} (26 - 20) = c_{z} (30 - 26) \Rightarrow 3 c_{y} = 2 c_{z}

These give

c_{x} : c_{y} : c_{z} = 4 : 6 : 9

. Mixing

x

and

z

at a common final temperature

T

4 (T - 10) = 9 (30 - T) \Rightarrow 13 T = 310

so the mixture settles at

T = 23.84^{\circ} C

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Single correct option