Final temperature of the water after adding heat?

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SUMMARY

The final temperature of water after adding 1500 calories of heat to 500 grams of water at an initial temperature of 22.5ºC is calculated using the equation Q=mcΔT. The correct approach involves recognizing that the total heat energy is the sum of the initial heat energy and the added heat. The final temperature is determined to be 25.5ºC, which is incorrect. The accurate final temperature, after considering the heat added, is 23.5ºC, calculated by using the heat equation properly without misinterpreting the initial temperature as a change in temperature.

PREREQUISITES
  • Understanding of the specific heat capacity of water (1.0 cal/gºC)
  • Familiarity with the heat transfer equation Q=mcΔT
  • Basic arithmetic skills for temperature calculations
  • Knowledge of calorie as a unit of heat energy
NEXT STEPS
  • Review the concept of specific heat capacity and its applications in thermal physics
  • Practice solving problems using the Q=mcΔT equation with varying masses and heat inputs
  • Explore the implications of heat transfer in different states of matter
  • Investigate common misconceptions in thermal energy calculations
USEFUL FOR

Students studying thermodynamics, physics educators, and anyone preparing for exams involving heat transfer and temperature calculations.

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Homework Statement


You add 1500 cal of heat to a cup of water at 22.5ºC. The water has a mass of 500.0g. What is the final temperature of the water?

Homework Equations


Q=mcΔT

The Attempt at a Solution


so i tried solving it by finding the energy of the water
Q=(500g)(1.0cal/g)(22.5ºC)
Q=11250 cals

then i tried adding 11250 cals to the 1500 cals that was added onto it from the problem and got 12750 cals.

using 12750 cals as Q, i set up Q=mcΔT and plugged in all the known variables and solved for change in T, which was 25.5ºC. I took this change in T and added it to the initial temperature of 22.5ºC, and got 48ºC for the final temperature of the water. Is that right? I didn't get an answer sheet and I have a test tomorrow so I have no idea if I'm doing this right or not
 
Physics news on Phys.org
It is not ##\Delta T## that is 22.5 °C - it is the initial temperature. You are asked to find the final temperature. What you are computing would be the heat required to heat the water by 22.5 °C from where it was initially.
 
A calorie is the amount of heat needed to increase the temperature of 1g of water by 1 degree, the problem is only to know the definition and simple arithmetic.
 

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