calculate the heat given up when 0.1kg of steam at 100¡ã© condenses to h20 at 40¡ã©(s.l.h of vaporisation = 2.2¡Á10^6) (c=4200)
To calculate the heat given up when 0.1kg of steam at 100°C condenses to H2O at 40°C, we need to consider the heat required for two processes:
1. Heating the steam from 100°C to its boiling point.
2. Condensing the steam at its boiling point to water at 40°C.
Let's break down the calculation step by step:
1. Heating the steam:
The formula to calculate the heat required to heat a substance is Q = mcΔT, where Q represents heat, m represents mass, c represents specific heat capacity, and ΔT represents the change in temperature.
Given:
- Mass (m) = 0.1 kg
- Specific heat capacity (c) = 4200 J/kg°C
- Initial temperature (T1) = 100°C
- Final temperature (T2) = 100°C (boiling point of steam)
Using the formula, we can calculate the heat required to heat the steam to its boiling point:
Q1 = (0.1 kg) × (4200 J/kg°C) × (100°C - 100°C)
Q1 = 0 J
Therefore, no heat is required to heat the steam from 100°C to its boiling point since its temperature remains constant during this phase change.
2. Condensing the steam:
The heat required to condense a substance can be calculated using the formula Q = mL, where Q represents heat, m represents mass, and L represents the specific latent heat of vaporization.
Given:
- Mass (m) = 0.1 kg
- Specific latent heat of vaporization (L) = 2.2 × 10^6 J/kg
Using the formula, we can calculate the heat required to condense the steam:
Q2 = (0.1 kg) × (2.2 × 10^6 J/kg)
Q2 = 220,000 J
Therefore, the heat given up when 0.1 kg of steam at 100°C condenses to water at 40°C is 220,000 J.
Note: This calculation assumes no heat is lost to the surroundings during the condensation process.