Question

Aaron wants to turn a 2.00 kg snowball into a gas. The snowball has an initial temperature of -14.1˚C. Find the total energy required to turn the snowball into a gas. Use the constants on the table at the bottom of the page for your calculations.

Answer 1

Given

mass of the snowball, m = 2 kg

initial temperature, T = -14.1 C

Now,

Specific heat capacity of ice under standard condition, C_ice = 2.108 KJ/kg C

Temperature of ice must be raised by 14.1 C to reach 0 C

hence, T = 14.1 C

Now, Energy required to raise the temperature by 14.1 C, E₁ = m*C_ice*T

=> E₁ = 2 * 2.108 * 14.1 = 59.446 kJ

Now ,

Latent heat of fusion, L₁ = 334 kJ / kg

Energy required to melt the ice, E₂ = m * L₁ = 2 * 336 = 668 kJ

Now

Specific heat capacity of water , C_water = 4.186 kJ/ kg C

temperature to raised from 0 C to 100 C to reach the boiling point

hence, T = 100 C

Energy required to raise the temperature of water from 0C to 100C, E₃ = m*C_water*T

=> E₃ = 2 * 4.186 * 100 = 837.2 kJ

Now,

Latent heat of vapourization of water, L₂ = 2258 kJ / kg

Energy required to convert water into vapour, E₄ = m*L₂ = 2 * 2258

=> E₄ = 4516 kJ

Now

Total energy required to convert 2kg of ice into gas = E₁ + E₂ + E₃ + E₄

=> E₁ + E₂ + E₃ + E₄ = 59.446 + 668 + 837.2 +4516

                                     = 6080.646 kJ

                                     = 6.080 MJ