2 kg of ice melts when water at $100^{\circ} C$ is poured in a hole drilled in a block of ice. What mass of water was used?
Given: Specific heat capacity of water is $4200 J k g^{- 1} K^{- 1}$ , specific latent heat of ice is $336 \times 10^{3} J K g^{- 1}$ .

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Solution

Step 1: Identifying the known and unknown
Given,
Mass of ice, $m_{1} = 2 k g$
Mass of water, $m$
Initial temperature of water,
$T_{1} = 100^{\circ} C = 373 K$
Final temperature of water,
$T_{2} = 0^{\circ} C = 273 K$
Specific heat capacity of water,
$c = 4200 J k g^{- 1} K^{- 1}$
Specific latent heat of ice,
$L = 336 \times 10^{3} J k g^{- 1}$

Step 2: Calculate the amount of heat required to convert ice into water at $0^{\circ} C$
Specific latent heat,
$L = \frac{Q}{m_{1}} (a t T = 0^{\circ} C)$
$\Rightarrow Q = m_{1} L$
Therefore,
$Q_{i c e} = (2 k g) \times (336000 J k g^{- 1})$
$Q_{i c e} = 672000 J$

Step 3: Calculate the amount of heat released by hot water to lower its temperature to $0^{\circ} C$
Specific heat capacity, $c = \frac{Q}{| m \times Δ T |}$
$\Rightarrow Q = m c | Δ T |$
$| Δ T | = | T_{2} - T_{1} |$
$| Δ T | = | 273 K - 373 K | = 100 K$
Therefore,
$Q_{w a t e r} = (m) \times (4200 J k g^{- 1} K - 1) \times (100 K)$
$\Rightarrow Q_{w a t e r} = 420000 m J$

Step 4: Calculation of mass
According to the principle of calorimetry,
$Q_{w a t e r} = Q_{i c e}$
$420000 m J = 672000 J$
$m = \frac{672000}{420000}$
$m = 1.6 k g$
The mass of water used was $1.6 k g$ .

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Q. 2 kg of ice melts when water at 100 C is poured in a hole drilled in a block of ice. what mass of water was used? specific heat capacity of water= 4200 Jkg^-1K^-1, L_ice = 336 x 10³ Jkg^-1.

10 kg

of ice completely melts when water at

100^{\circ} C

is poured into a hole drilled in the ice. If the specific heat capacity of water is

4200 {J kg}^{- 1}^{\circ} C^{- 1}

and the specific latent heat of melting of ice is

336 \times 10^{3} {J kg}^{- 1}

, the amount of the water needed is

250 g

of water at

30^{\circ} C

is contained in a copper vessel of mass

50 g

. Calculate the mass of ice required to bring down the temperature of the vessel and its contents to

5^{\circ} C

. Given specific latent heat of fusion of ice is

336 \times 10^{3} J k g^{- 1}

, specific heat capacity of copper is

400 J k g^{- 1} K^{- 1}

, and the specific heat capacity of water is

4200 J k g^{- 1} K^{- 1}

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Density

Standard VIII Physics

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2 kg of ice melts when water at 100∘C is poured in a hole drilled in a block of ice. What mass of water was used? Given: Specific heat capacity of water is 4200 J kg−1 K−1, specific latent heat of ice is 336×103 J Kg−1.

2 kg of ice melts when water at $100^{\circ} C$ is poured in a hole drilled in a block of ice. What mass of water was used?
Given: Specific heat capacity of water is $4200 J k g^{- 1} K^{- 1}$ , specific latent heat of ice is $336 \times 10^{3} J K g^{- 1}$ .