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In an insulated vessel, a quantity of hot water at temperature t1 is mixed with a different quantity of cold water at temperature t2. after equilibrium is established, the vessel contains __________.

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In an insulated vessel, a quantity of hot water at temperature T1 is mixed with a different quantity of cold water at temperature T2. After equilibrium is established, the vessel contains water only.

Answer:water at a common temperature T

Explanation:

Let say First quantity be \(m_1\) and second Quantity be \(m_2\)

and their specific heat be c

thus balancing heat so that total mass of water has a common temperature of T

\(m_1c(T-T_1)=m_2c(T_2-T)\)

let \(\frac{m_1}{m_2}=x\)

\(xT-xT_1=T-T_2\)

\(T=\frac{T_2-xT_1}{x-1}\)

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