# Difficult question big reward what will be the temperature of the mixture if you mix 40 liters of water at a temperature

Difficult question big reward what will be the temperature of the mixture if you mix 40 liters of water at a temperature of 10 degrees with 40 liters of water at a temperature of 70 degrees

Given: Vx (volume of cold water) = 40 l = Vg (volume of hot water); tx (cold water temperature) = 10 ºС; tg (hot water temperature) = 70 ºС.

Since the same volumes of water were mixed, the steady-state temperature can be determined by the formula: t = (tх + tg) / 2 = (10 + 70) / 2 = 40 ºС.

Proof: Q1 = Q2.

C * mx * (t – tx) = C * mg * (tg – t).

C * ρ * Vх * (t – tх) = C * ρ * Vg * (tg – t).

t – tx = tg – t.

2t = tg + tx and t = (tg + tx) / 2 (true).

Answer: The temperature of the mixture is 40 ºС.

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