The temperature of equal masses of three different liquids x, y and z are 10 ° C, 20 ° C and 30 ° C respectively. The temperature of mixture when x is mixed with y is 16 ° C and that when y is mixed with z is 26 ° C. The temperature of mixture when x and z are mixed will be: (a) 28.32 ° C (b) 25.62 ° C (c) 23.84 ° C (d) 20.28 ° C

Answer: (c). Equal masses: x and y: cx(16 - 10) = cy(20 - 16) ⇒ cy = 1.5cx. y and z: cy(26 - 20) = cz(30 - 26) ⇒ cz = 1.5cy = 2.25cx. x and z: cx(T - 10) = 2.25cx(30 - T) ⇒ 3.25T = 77.5 T ≈ 23.84°C So the answer is (c) 23.84°C.

The temperature of equal masses of three different liquids x, y and z… | JEE Main 2021 (26 Aug, Shift 2)

Q29JEE Main 2021 · 26 AUG · SHIFT 2Medium

Calorimetry, Latent Heat & Mechanical Equivalent of Heat

The temperature of equal masses of three different liquids x, y and z are 10 $^{\circ}$ C, 20 $^{\circ}$ C and 30 $^{\circ}$ C respectively. The temperature of mixture when x is mixed with y is 16 $^{\circ}$ C and that when y is mixed with z is 26 $^{\circ}$ C. The temperature of mixture when x and z are mixed will be:

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Answer: (c)

Equal masses: x and y: $c_x(16 - 10) = c_y(20 - 16) \Rightarrow c_y = 1.5c_x$ .
y and z: $c_y(26 - 20) = c_z(30 - 26) \Rightarrow c_z = 1.5c_y = 2.25c_x$ .
x and z: $c_x(T - 10) = 2.25c_x(30 - T) \Rightarrow 3.25T = 77.5$
$T \approx 23.84^{\circ}\text{C}$
So the answer is (c) $23.84^{\circ}\text{C}$ .

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