A non-conducting vessel contains a liquid of mass 70 g at 25º C. Another 70.0g of the same liquid at 35ºC is…

Analyze the question

Two equal masses of the same liquid at different temperatures are mixed in a non-conducting (insulated) vessel. We want the final equilibrium temperature.

Concept

With no heat lost to the surroundings (and the vessel absorbing no heat), the principle of conservation of heat energy applies:

Heat lost by the hot liquid = Heat gained by the cold liquid

Heat is given by Q = mcΔθ, where m is mass, c is specific heat capacity, and Δθ is the temperature change.

Solution

Let the final temperature be θ.

• Cold liquid gains heat: Q₁ = 70 × c × (θ − 25)
• Hot liquid loses heat: Q₂ = 70 × c × (35 − θ)

Setting Q₁ = Q₂:

70c(θ − 25) = 70c(35 − θ)

The 70c cancels on both sides:

θ − 25 = 35 − θ 2θ = 60 θ = 30 °C

This agrees with the mean of the two temperatures: (25 + 35)/2 = 30 °C. That is expected, because the masses and the liquid are the same.

Answer: C. 30 °C.

Tip

When equal masses of the same substance are mixed, the final temperature is simply the average of the two starting temperatures. You can skip the long working and save time in the exam. If the masses are different, use the full equation: θ = (m₁θ₁ + m₂θ₂)/(m₁ + m₂).