An insulating container contains 250 g of water at 20°C. Steam at 100°C is passed through it, heating it up to 25°C. During this process, part of the steam also gets condensed, raising the mass of water to 252 g. If the specific heat of water is \(1\ \text{Cal}\ g^{-1}\ °C^{-1}\), then what is the value of the latent heat of steam?
550 Cal/g
Heat gained by the water (mass 250 g) as it warms from 20°C to 25°C:
\(Q_{water} = mc\Delta T = 250 \times 1 \times (25-20) = 1250\ \text{Cal}\)
Mass of steam that condensed: \(m_{steam} = 252 - 250 = 2\ \text{g}\). This condensed steam first releases its latent heat at 100°C and then cools (as liquid water) from 100°C to the final temperature 25°C:
\(Q_{steam} = m_{steam}L + m_{steam}c(100-25) = 2L + 2\times1\times75 = 2L+150\)
Since the container is insulating (no heat lost to surroundings), heat lost by the steam equals heat gained by the water:
\(2L + 150 = 1250 \Rightarrow 2L = 1100 \Rightarrow L = 550\ \text{Cal/g}\)
Hence the latent heat of steam is 550 Cal/g, option (c).
Similar Questions
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Important Questions from Calorimetry
A copper block of mass 3 kg is heated in a furnace to a temperature of 450° C and then placed on a large ice block. Find the maximum amount of ice that can melt? (specific heat of copper = 0.39 Jg-1K-1, heat of fusion of water = 335 Jg-1K-1)
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Which of the following statements is INCORRECT for heat?
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