How much energy is required to change a 58 g ice cube from ice at −1◦C to steam at 101◦C? The specific heat of ice is 2090 J/kg ·◦ C and of water 4186 J/kg ·◦ C. The latent heat of fusion of water is 3.33 × 105 J/kg, its latent heat of vaporization is 2.26 × 106 J/kg, and the specific heat of steam is 2010 J/kg ·◦ C.
Answer in units of MJ
c₁=2090 J/kg ,c₂ = 4186 J/kg •◦ C,
c₃ =2010 J/kg •◦ C.
λ = 3.33•10^5 J/kg, r = 2.26• 10^6 J/kg.
m=0.058 kg
Q= c₁m(1)+ λm +c₂m(100) +rm + c₃m(1) = …(J)
1MJ = 10⁶J
To calculate the energy required to change the ice cube from ice at -1°C to steam at 101°C, we need to consider the different steps involved in the phase changes.
1. Heating the ice cube from -1°C to 0°C:
The energy required can be calculated using the specific heat capacity of ice:
q1 = mass × specific heat capacity × change in temperature
= 58 g × 2090 J/kg·°C × (0°C - (-1°C))
= 58 g × 2090 J/kg·°C × 1°C
= 121,220 J
2. Melting the ice at 0°C to water at 0°C:
We need to consider the latent heat of fusion of water:
q2 = mass × latent heat of fusion
= 58 g × 3.33 × 10^5 J/kg
= 19,314,000 J
3. Heating the water from 0°C to 100°C:
The energy needed can be calculated using the specific heat capacity of water:
q3 = mass × specific heat capacity × change in temperature
= 58 g × 4186 J/kg·°C × (100°C - 0°C)
= 244,052 J
4. Vaporizing the water at 100°C to steam at 100°C:
We need to consider the latent heat of vaporization:
q4 = mass × latent heat of vaporization
= 58 g × 2.26 × 10^6 J/kg
= 131,080,000 J
5. Heating the steam from 100°C to 101°C:
The energy required can be calculated using the specific heat capacity of steam:
q5 = mass × specific heat capacity × change in temperature
= 58 g × 2010 J/kg·°C × (101°C - 100°C)
= 117,858 J
To get the total energy required, we sum up all the individual steps:
Total energy = q1 + q2 + q3 + q4 + q5
= 121,220 J + 19,314,000 J + 244,052 J + 131,080,000 J + 117,858 J
= 150,877,130 J
The answer can be converted to megajoules (MJ) by dividing by 1,000,000:
Total energy = 150,877,130 J / 1,000,000
= 150.87713 MJ
Therefore, the energy required to change the 58 g ice cube from ice at -1°C to steam at 101°C is approximately 150.88 MJ.