Given:
cp,ice = 2090 J/kg◦C
cp,water = 4186 J/kg ·◦C
cp,steam = 2010 J/kg ◦C
Lf = 3.33 × 105 J/kg
Lv = 2.26 × 106 J/kg
How much energy is required to change a
37 g ice cube from ice at −10◦C to steam at
116◦C? Answer in units of J.
ok.. so this is how i worked it out
37g(2090)(10C)=773300J
37g(3.33*10^5)=12321000J
37g(4186)(100)=15488200J
37g(2.26*10^6)=83620000J
37g(2010)(116-100)=1189920J
i added all of them together and i got
113392420J.
is this right?
113,392,420 J looks good to me.
Your approach is mostly correct, but there are a couple of errors in your calculation. Let's go through the steps together:
1. First, calculate the energy required to heat the ice from -10°C to its melting point at 0°C, using the specific heat capacity of ice:
Energy = mass * specific heat capacity (ice) * temperature change
Energy = 37g * 2090 J/kg°C * (0°C - (-10°C)) = 37g * 2090 J/kg°C * 10°C = 773,300 J
2. Next, calculate the energy required to melt the ice at 0°C into water at 0°C, using the latent heat of fusion (Lf):
Energy = mass * latent heat of fusion
Energy = 37g * 3.33 x 10^5 J/kg = 12,321,000 J
3. Then, calculate the energy required to heat the water from 0°C to its boiling point at 100°C, using the specific heat capacity of water:
Energy = mass * specific heat capacity (water) * temperature change
Energy = 37g * 4186 J/kg°C * (100°C - 0°C) = 154,882,000 J
4. Now, calculate the energy required to vaporize the water at 100°C into steam at 100°C, using the latent heat of vaporization (Lv):
Energy = mass * latent heat of vaporization
Energy = 37g * 2.26 x 10^6 J/kg = 83,620,000 J
5. Finally, calculate the energy required to heat the steam from 100°C to the final temperature of 116°C, using the specific heat capacity of steam:
Energy = mass * specific heat capacity (steam) * temperature change
Energy = 37g * 2010 J/kg°C * (116°C - 100°C) = 1,189,920 J
Now, add up all the energies calculated in steps 1 to 5:
Total Energy = 773,300 J + 12,321,000 J + 154,882,000 J + 83,620,000 J + 1,189,920 J = 252,786,220 J
Therefore, the correct answer is 252,786,220 J, not 113,392,420 J as you calculated.