If 1 liter of water at 40°C is mixed with 1 liter of water at 50°C, what will be the temperature of the resulting mixture?

Correct option is C

The correct answer is option (c) Between 40°C and 50°C.

Explanation

When two substances at different temperatures are mixed, the final temperature of the mixture depends on the mass and specific heat capacity of the substances, assuming no heat is lost to the surroundings. In this case, both quantities are identical for the two bodies of water. Therefore, the heat lost by the warmer water (at 50°C) will equal the heat gained by the cooler water (at 40°C), and the system will reach thermal equilibrium. The final temperature will lie between the two initial temperatures (40°C and 50°C). Specifically, it will be the average of the two, which can be calculated as:

Tfinal=(T1+T2)2=(40°C+50°C)2=45°CT_{\text{final}} = \frac{(T_1 + T_2)}{2} = \frac{(40°C + 50°C)}{2} = 45°CTfinal​=2(T1​+T2​)​=2(40°C+50°C)​=45°C

However, the option that best describes the outcome (given that the mixture will naturally be between the two initial temperatures) is option (c).

Information Booster

• Thermal equilibrium occurs when the heat gained by the cooler object equals the heat lost by the warmer object.

• The specific heat capacity of water is consistent, meaning it requires the same amount of energy to change the temperature of a given mass of water.

• The process of mixing liquids at different temperatures results in energy transfer between them, until a common temperature is reached.

• In practice, the final temperature will always be between the two initial temperatures, assuming equal masses of water.

• The formula used to calculate the final temperature assumes no heat loss to the surroundings.

​