A piece of ice of mass 50 g exists at a temperature of -20-C- Determine the total heat required to convert it completely to steam at 100- C- Specific heat capacity of ice -0-5 cal-g-C- specific latent heat of fusion for ice - 80 cal-g and specific latent heat of vapourisation for water - 540 cal-g

Formula used: Q=mL, Q=msΔ T Given: m=50 g, T_i= 20^∘C, T_f=100^∘C, s_i=0.5 cal/g^∘C, L_f= 80 cal/g, L_v=540 cal/g For changing ice at 20^∘C to steam ...

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Standard VII

Physics

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A piece of ic...

Question

A piece of ice of mass $50 g$ exists at a temperature of $- 20^{\circ} C$ . Determine the total heat required to convert it completely to steam at $100^{\circ} C$ . (Specific heat capacity of ice $= 0.5 c a l / g^{\circ} C$ ; specific latent heat of fusion for ice $= 80 c a l / g$ and specific latent heat of vapourisation for water $= 540 c a l / g$ )

36500 c a l

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12400 c a l

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26500 c a l

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46500 c a l

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Solution

The correct option is A $36500 c a l$
Formula used: $Q = m L, Q = m s Δ T$
Given: $m = 50 g, T_{i} = - 20^{\circ} C, T_{f} = 100^{\circ} C, s_{i} = 0.5 c a l / g^{\circ} C, L_{f} = 80 c a l / g, L_{v} = 540 c a l / g$

For changing ice at $- 20^{\circ} C$ to steam at $100^{\circ} C$ , the complete process is achieved in four different stages:

(i) The rise in temperature of ice from $- 20^{\circ} C$ to $0^{\circ} C$ (i.e., melting point of ice).
Heat required for this process
$Δ Q_{1} = m s (0 - (- 20))$
$Δ Q_{1} = (50) (0.5) (0 - (- 20)) = 500 c a l$

(ii)The melting of ice at $0^{\circ} C$
Heat required for this process
$Δ Q_{2} = m L$
$Δ Q_{2} = (50) (80) = 4000 c a l$

(iii) The rise in temperature of melted ice (i.e., water) from $0^{\circ} C$ to $100^{\circ} C$ (i.e., B.P. of water)
Heat required for this process
$Δ Q_{3} = m s_{w} (100 - 0)$
$Δ Q_{3} = (50) (1) (100) = 5000 c a l$

(iv) The vapourisation of water at $100^{\circ} C$
Heat required for this process
$Δ Q_{4} = m L$
$Δ Q_{4} = (50) (540) = 27000 c a l$

$∴$ Total heat required $Q = Δ Q_{1} + Δ Q_{2} + Δ Q_{3} + Δ Q_{4} = 36500 c a l$

FINAL ANSWER: (c).

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Similar questions

Q. The amount of heat required to convert

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c_{i} = 0.5 {cal g}^{- 1}^{\circ} C^{- 1}

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