The amount of heat, Q, that is required to raise the temperature of a substance can be calculated using the formula: Q = mc(Tf – Ti) where m is the mass of the substance in grams, c is the specific heat capacity of the substance, and Tf and Ti are the final and initial temperatures of the substance in Celsius, respectively. The specific heat capacity of water is 4.19 J/g°C. What amount of heat, in J, is required to raise the temperature of 57 g of water from 25°C to 64°C? Enter your answer rounded to the nearest whole number.
The Correct Answer and Explanation is:
The formula to calculate the heat required to raise the temperature of a substance is:Q=mc(Tf−Ti)Q = mc(T_f – T_i)Q=mc(Tf−Ti)
Where:
- QQQ is the heat required (in joules),
- mmm is the mass of the substance (in grams),
- ccc is the specific heat capacity of the substance (in joules per gram per degree Celsius),
- TfT_fTf is the final temperature (in °C),
- TiT_iTi is the initial temperature (in °C).
Given:
- m=57 gm = 57 \, \text{g}m=57g (mass of water),
- c=4.19 J/g°Cc = 4.19 \, \text{J/g°C}c=4.19J/g°C (specific heat capacity of water),
- Ti=25 °CT_i = 25 \, \text{°C}Ti=25°C (initial temperature),
- Tf=64 °CT_f = 64 \, \text{°C}Tf=64°C (final temperature).
Now, plug these values into the formula:Q=57×4.19×(64−25)Q = 57 \times 4.19 \times (64 – 25)Q=57×4.19×(64−25)
First, calculate the temperature difference:Tf−Ti=64−25=39 °CT_f – T_i = 64 – 25 = 39 \, \text{°C}Tf−Ti=64−25=39°C
Now calculate QQQ:Q=57×4.19×39Q = 57 \times 4.19 \times 39Q=57×4.19×39Q=57×163.41Q = 57 \times 163.41Q=57×163.41Q=9304.37 JQ = 9304.37 \, \text{J}Q=9304.37J
Rounded to the nearest whole number:Q≈9304 JQ \approx 9304 \, \text{J}Q≈9304J
So, the amount of heat required to raise the temperature of 57 g of water from 25°C to 64°C is approximately 9304 J.
Explanation:
- Specific heat capacity ccc is a property of the material that indicates how much heat is required to raise the temperature of 1 gram of the substance by 1°C.
- The formula Q=mc(Tf−Ti)Q = mc(T_f – T_i)Q=mc(Tf−Ti) calculates the amount of heat required based on the mass of the substance, the specific heat, and the change in temperature.
- Since water has a relatively high specific heat capacity (4.19 J/g°C), it requires a significant amount of energy to heat up by even a small temperature difference.
This formula is widely used in calorimetry to calculate energy changes in different substances when heated or cooled.
