Calculate the amount of heat required to convert 200g of water, which is at the temperature of 50°C to steam at 110°C at normal pressure. Specific heat capacity of water = 4200 J/kg-K, latent heat of vaporization of water = 2.25 × 106 J/kg, Specific heat capacity of steam = 2000 J/kg-K.?

Option 1 : 4.96 × 104 Joule

CONCEPT:

• Specific heat or specific heat capacity of a body is the amount of heat required for a unit mass of the body to raise the temperature by 1 degree Celsius.
• • It is denoted by “c” or “s”.
  • It is different for each substance.
  • Its unit is cal/g-°C in CGS and joule/g-K in SI unit.
  • 1 calorie = 4.186 Joule.
  • s = (Q /m Δ t) .

• Specific latent heat of fusion and vaporization:

• In the process of melting or vaporization, the temperature remains constant. The amount of heat needed to change the state of matter having mass m is-
• Q = m L
• Latent heat of fusion: It is the heat required for 1 kg of substance to change it from solid to liquid state without change of temperature.
  • Latent heat of fusion of ice = 3.36 × 10⁵ J/kg
    • In CGS = 80 cal/gm.
• Latent heat of Vaporization: It is the heat required for 1 kg of substance to change it from liquid to gaseous state without change of temperature.
  • Latent heat of vaporization of water = 2.25 × 10⁶ J/kg.
    • In CGS = 536 cal/gm

CALCULATION:

Given, mass of water = 200g = 0.2 kg.

Flow chart

(Liquid Water at 50°C) → (Liquid Water at 100° C) → (Latent heat of vaporization) → (Gaseous water at 100° C) → (Gaseous water at 110° C)

Heat required to bring water at 100° C = Q = m s ΔT = (0.2kg) (4200 J/kg-K) (50K) = 42,000 J

Heat required to make water 100° C to water 100° C gas = (0.2kg) (2.25 × 10⁶ J/kg-K) = 4,50,000 J

Heat required to make water gas 100° C to water 110° C gas = (0.2kg) (2000 J/kg-K) (10K) = 4,000 J

Total Heat needed to convert 50°C (water) to steam at 110°C = 42000 + 450000 + 4000 = 49600 J

⇒ 4.96 × 10⁴ Joule