Heating and Cooling Curve Problems

Question

Calculate the energy (in kJ) required to raise the temperature of 1.00 g H2O 

from -25.00C to-11.00C.

Calculate the energy (in kJ) required to raise the temperature of 1.00 g H2O 

from -15.00C to 22.00C

Calculate the energy (in kJ) required to raise the temperature of 1.00g H2O

from 25.00◦C to 57.00°C.

Calculate the energy (in kJ) required to raise the temperature of 1.00g H2O 

from 60.0C to 120.0C.

Calculate the energy (in kJ) required to raise the temperature of 1.00g H2O

from -10.0◦C to 120.0C.

Answer 1

For the following calculations, several formulae will be used, along with several constants. The constants used here may vary slightly from ones you have or are given, so final answers may be sightly different.

q = mC∆T where q = heat; m = mass; C = specific heat; ∆T = change in temperature

q = m∆Hf where q = heat; m = mass; ∆Hf = heat of fusion

q = m∆Hvap where q = heat; m= mass; ∆Hvap = heat of vaporization

C_ice = 2.09 J/gº

C_liquid = 4.184 J/gº

C_steam = 1.89 J/gº

∆Hf = 334 J/g

∆Hvap = 2260 J/g

Calculate the energy (in kJ) required to raise the temperature of 1.00 g H2O from -25.00C to-11.00C.

q = mC∆T

q = (1.00 g)(2.09 J/gº)(14º)

q = 29.26 J = 0.0293 kJ (3 sig.figs.)

Calculate the energy (in kJ) required to raise the temperature of 1.00 g H2O from -15.00C to 22.00C

step 1. Raise temp from - 15.00º to 0º

q = mC∆T = (1.00 g)(2.09 J/gº)(15º) = 31.35 J

step 2. Melt ice at 0º

q = m∆Hf = (1.00 g)(334 J/g) = 334 J

step 3. Raise temp from 0º to 22.00º

q = mC∆T = (1.00 g)(4.184 J/gº)(22º) = 92.05 J

step 4. Add up all the heats and convert to kJ:

31.35 J + 334 J + 92.05 J = 457 J = 0.457 kJ (3 sig.figs.)

Calculate the energy (in kJ) required to raise the temperature of 1.00g H2O from 25.00◦C to 57.00°C

q = mC∆T = (1.00 g)(4.184 J/gº)(32º) = 133.88 J = 0.134 kJ (3 sig.figs.)

Calculate the energy (in kJ) required to raise the temperature of 1.00g H2O from 60.0C to 120.0C

step 1. Raise temp from 60.0º to 100º

q = mC∆T = (1.00 g)(4.184 J/gº)(40º) = 167.36 J

step 2. Convert liquid water to gas (steam) at 100ºC

q = m∆Hvap = (1.00 g)(2260 J/g) = 2260 J

step 3. Heat steam from 100º t0 120º

q = mC∆T = (1.00 g)(1.89 J/gº)(20º) = 37.8 J

step 4. Add up all the heats and convert to kJ

167.36 J + 2260 J + 37.8 J = 2465 J = 2.47 kJ (3 sig.figs.)

Calculate the energy (in kJ) required to raise the temperature of 1.00g H2O from -10.0◦C to 120.0C

Simply follow the steps outlined below as done above in the other problems.

step 1. Raise temp from -10º to 0º q = mC∆T

step 2. Melt ice at 0º q = m∆Hf

step 3. raise temp of liquid water from 0º to 100º q = mC∆T

step 4. convert liquid to steam q = m∆Hvap

step 5. raise temp of steam from 100º to 120º q = mC∆T

step 6. add up all the heats and convert to kJ