What is the difference in the amount of heat given out by 4kg of steam and 4kg of water when both are cooled from 100ºC to 80ºC? [the specific latent heat of steam is 2,260,000Jkg\(^{-1}\), specific heat capacity of water is 4200Jkg\(^{-1}\)K\(^{-1}\)]
To find the difference in the amount of heat given out by 4 kg of steam and 4 kg of water when both are cooled from 100°C to 80°C, we need to calculate the heat released by each.
Heat Given Out by Water
The heat given out by water as it cools can be calculated using the formula:
\(Q = mc\Delta T\)
Where:
- m = 4 kg (mass of water)
- c = 4200 (specific heat capacity of water)
- \( \Delta\) T = 100 - 80 = 20K (change in temperature)
Calculating the heat given out by water:
\(Q_{\text{water}} = 4 \times 4200 \times 20 = 336,000 \, \text{J}\)
Heat Given Out by Steam
For steam, we need to consider both the cooling of the steam to water and the cooling of the water from 100°C to 80°C. The total heat given out by the steam is the sum of the heat released during condensation and the heat released during cooling.
Heat released during condensation: \(Q_{\text{condensation}} = mL\)
Where:
- \( L = 2,260,000 \, \text{J/kg} \) (specific latent heat of steam)
Calculating the heat released during condensation:
\(Q_{\text{condensation}} = 4 \, \text{kg} \times 2,260,000 \, \text{J/kg} = 9,040,000 \, \text{J}\)
Heat released by water as it cools from 100°C to 80°C:
This is the same calculation we did for water above:
\(Q_{\text{cooling}} = 4 \times 4200 \times 20 = 336,000 \, \text{J}\)
Total heat given out by steam:
\(Q_{\text{steam}} = Q_{\text{condensation}} + Q_{\text{cooling}} = 9,040,000 \, \text{J} + 336,000 \, \text{J} = 9,376,000 \, \text{J}\)
Difference in Heat Given Out
Now, we find the difference in heat given out by steam and water:
\(\text{Difference} = Q_{\text{steam}} - Q_{\text{water}} = 9,376,000 \, \text{J} - 336,000 \, \text{J} = 9,040,000 \, \text{J}\)
The difference in the amount of heat given out by 4 kg of steam and 4 kg of water when both are cooled from 100°C to 80°C is 9,040,000 J.
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