In two glasses there is liquid of the same type. The first has volume V 1 and temperature T 1 , and the second volume V 2 and temperature T 2 . We mix the liquids and wait for the temperature

Question

In two glasses there is liquid of the same type. The first has volume V 1 ​ and temperature T 1 ​ , and the second volume V 2 ​ and temperature T 2 ​ . We mix the liquids and wait for the temperature to settle. What is the common temperature if heat loss is neglected?

TestHub · Accepted Answer

Using the source's constant-density and specific-heat approximation, heat balance gives
$m_{1} = ρ V_{1}, m_{2} = ρ V_{2}$
$m_{1} c (T - T_{1}) = m_{2} c (T_{2} - T)$
$V_{1} (T - T_{1}) = V_{2} (T_{2} - T)$
$T = \frac{T _{1} V _{1} + T _{2} V _{2}}{V _{1} + V _{2}}$

Physics - Heat & Thermo Question with Solution | TestHub

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JEE Main 2028 (Class 11)