Question

Energy in the amount of 420 J is added to a 35 g sample of water at a temperature of 10°C. What is the final temperature of the water?

Answer 1

The final temperature of the water, T2 = 38.57°C

Temperature can be defined as a measure of the degree of hotness or coldness of a physical object (body). Thus, it is measured with a thermometer and its units are degree Celsius (°C), Fahrenheit (°F) and Kelvin (°K).

A calorie refers to the amount of heat required to raise the temperature of a gram of water by one (1) degree Celsius (1°C).

Given the following data:

• Quantity of energy = 420J

• Mass = 35 grams

• Initial temperature, T1 = 10°C

The specific heat capacity of water is 4.2 J/g°C.

To find the final temperature of the water (T2):

Mathematically, the quantity of energy (heat capacity) is given by the formula;

$Q = mcdt$

Where;

• Q represents the heat capacity or quantity of heat.

• M represents the mass of an object.

• C represents the specific heat capacity of water.

• dt represents the change in temperature.

Substituting the values into the formula, we have;

$420 = 3.5 \; * \; 4.2 \; * \; dt$

$420 = 14.7 \; * \; dt\\\\dt = \frac{420}{14.7}$

Change in temperature, dt = 28.57°C

Next, we would solve for the final temperature by using this formula;

$dt = T2 - T1$

$28.57 = T_{2} - 10\\\\T_{2} = 28.57 \; + \; 10\\\\T_{2} = 38.57$

Final temperature, T2 = 38.57°C

Therefore, the final temperature of the water, T2 is equal to 38.57°C

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