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QJEEM21Phe6e2: JEE Main 2021 Physics - Class 11 JEEM21Phe6e2 Solution: The temperature of equal masses of three different liquids x, y …

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 :

Multiple Choice Options

  • A 28.32 ∘^\circ C
  • B 25.62 ∘^\circ C
  • C 23.84 ∘^\circ C
  • D 20.28 ∘^\circ C

Step-by-Step Verified Solution

JEE Main 2021 (Online) 26th August Evening Shift Physics - Heat and Thermodynamics Question 200 English Explanation

when x and y are mixed, Tf1 = 16 ∘^\circ C

m1s1T + m2s2T2 = (m1s1 + m2s2)Tf1

s1 ×\times 10 + s2 ×\times 20 = (s1 + s2) ×\times 16

s1 = 23{2 \over 3} s2 .... (i)

when y and z are mixed, Tf2 = 26 ∘^\circ C

m2s2T + m3s3T3 = (m3s3 + m3s3)Tf2

s2 ×\times 20 + s3 ×\times 30 = (s2 + s3) ×\times 26

s3 = 32{3 \over 2} s2 ..... (ii)

when x and z are mixed

m1s1T1 + m3s3T3 = (m1s1 + m3s3)Tf

23{2 \over 3} s2 ×\times 10 + 23{2 \over 3} s2 ×\times 20 = (23s2+32s2)Tf\left( {{2 \over 3}{s_2} + {3 \over 2}{s_2}} \right){T_f}

Tf = 23.84 ∘^\circ C

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