A steam at $100^{o} C$ is passed into $1 k g$ of water contained in a calorimeter of water equivalent $0.2 k g$ at $9^{o} C$ , till the temperature of the calorimeter and water in it is increased to $90^{o} C$ . The mass of steam condensed in $k g$ is nearly:
[sp. heat of water $= 1$ $c a l / g^{o}$ C, latent heat of vaporisation $= 540 c a l / g$

0.81

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0.18

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0.27

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0.54

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Solution

The correct option is B $0.18$
Initial temperature of calorimeter and water $T_{i} = 9^{o} C$
Final temperature of calorimeter and water $T_{f} = 90^{o} C$
$∴$ change in temperature: $Δ T = 90 - 9 = 81^{o} C$
Latent heat of vaporisation: $L_{v} = 540 c a l / g$
Mass of water present: $m_{w} = 1 k g = 1000 g$
Water equivalent of calorimeter is $0.2 k g = 200 g$
$∴$ $m_{c} S_{c} = 200 \times S_{w} = 200 \times 1 = 200$

Let the mass of steam condensed be $m_{s} g$
$∴$ $m_{s} L_{v} = (m_{w} S_{w} + m_{c} S_{c}) Δ T$
OR $m_{s} \times 540 = (1000 \times 1 + 200) \times 81$ $⟹ m_{s} = 180 g$
Thus mass of steam condensed is $0.18 k g$

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Similar questions

Steam at $100^{o} C$ is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at $15^{o} C$ till the temperature of the calorimeter and its contents rises to $80^{o} C .$ The mass of the steam condensed in kg is

Specific heat of water = $1 k c a l / k g^{\circ} C$ , Latent heat of Vaporisation = $540 k c a l / k g$

latent heat of vaporization of water = $540 c a l k g^{-} 1$ , specific heat capacity of water = $10^{3} c a l k g^{-} 1^{\circ} C^{-} 1$

500 g

of water and

100 g

of ice at

0^{o} C

are in a calorimeter whose water equivalent is

40 g

10 g

of steam at

100^{o} C

added to it. Then water in the calorimeter is (Latent heat of ice

= 80 c a l / g

, Latent heat of steam

= 540 c a l / g

)

Q. Steam at

100^{o} C

is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at

15^{o} C

till the temperature of the calorimeter and its contents rises to

80^{o} C .

The mass of the steam condensed in kg is

(IIT JEE 1986)

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A steam at 100oC is passed into 1 kg of water contained in a calorimeter of water equivalent 0.2 kg at 9oC, till the temperature of the calorimeter and water in it is increased to 90oC. The mass of steam condensed in kg is nearly:[sp. heat of water=1 cal/goC, latent heat of vaporisation =540 cal/g