Question

How much heat transfer in kJ is necessary to raise the temperature of a 0.347 kg piece of ice from -12.6ºC to 132.1ºC , including the energy needed for phase changes? (cice = 2090 J/kgºC, cwater = 4186 J/kgºC, csteam = 1520 J/kg, Lvap = 2256 kJ/kg, and Lfus = 334 kJ/kg)

Answer 1

given

mass m = 0.347 kg

piece of ice from -12.6ºC to 132.1ºC

C_ice = 2090 J/kgºC,

C_water = 4186 J/kgºC,

C_steam = 1520 J/kg,

L_vap = 2256 kJ/kg

and L_fus = 334 kJ/kg

so the total heat can be written as

Q = the energy needed for -12.6^oC to0^oC

+ energy needed for L_fus

+ energy needed for 0^oC water to 100^oC

+ energy needed for 100^oC water to 100^o C vapour

+ energy needed for 100⁰C to 132.1^oC

Q = m C_ice ( 12.6 ) + m L_fus + m C_water X 100 + m L_vap + m C_steam ( 132.1 - 100 )

Q = 0.347 ( 2090 X 12.6 + 334000 + 4186 X 100 + 2256000 + 1520 X 32.1 )

Q = 0.347 ( 26334 + 334000 + 418600 + 2256000 + 48792 )

Q = 0.347 X 3083726

Q = 1070052.922 J

Q = 1.070052922 X 10⁶ J

the energy needed for phase changes is Q = 1.070052922 X 10⁶ J