7. 50g of steam at 100 degree centigrade is passed into a mixture of 100g of ice and 200gm of water at 0 degree centigrade. Find the rise in temperature. (S.L. H. Of steam = 540 cal/g and Lf of ice = 80cal/g)

To find the rise in temperature, we need to calculate the amount of heat transferred between the steam and the mixture of ice and water.

First, let's calculate the heat absorbed by the ice to raise its temperature from 0°C to its melting point:

Heat absorbed by ice (Q1) = mass of ice (m1) × specific heat capacity of ice (c1) × change in temperature (ΔT1)

Given:
- mass of ice (m1) = 100 g
- specific heat capacity of ice (c1) = 1 cal/g°C (assuming ice is in liquid state at 0°C)
- change in temperature (ΔT1) = melting point of ice = 0°C

Q1 = 100g × 1 cal/g°C × 0°C = 0 cal

Next, let's calculate the heat absorbed by the ice to melt it into water:

Heat absorbed by ice (Q2) = mass of ice (m1) × heat of fusion of ice (Lf)

Given:
- mass of ice (m1) = 100 g
- heat of fusion of ice (Lf) = 80 cal/g

Q2 = 100g × 80 cal/g = 8000 cal

Now, let's calculate the heat absorbed by the water to raise its temperature from 0°C to the final temperature:

Heat absorbed by water (Q3) = mass of water (m2) × specific heat capacity of water (c2) × change in temperature (ΔT2)

Given:
- mass of water (m2) = 200 g
- specific heat capacity of water (c2) = 1 cal/g°C (assuming water is in liquid state)
- change in temperature (ΔT2) = final temperature - melting point of ice = final temperature - 0°C

Q3 = 200g × 1 cal/g°C × ΔT2

Finally, let's calculate the heat released by the steam to condense into water at 100°C:

Heat released by steam (Q4) = mass of steam (m3) × heat of condensation of steam (H)

Given:
- mass of steam (m3) = 50 g
- heat of condensation of steam (H) = 540 cal/g

Q4 = 50g × 540 cal/g = 27000 cal

Since the total heat absorbed by the ice and water is equal to the total heat released by the steam, we have:

Q1 + Q2 + Q3 = Q4

0 + 8000 + (200g × 1 cal/g°C × ΔT2) = 27000

8000 + ΔT2 = 27000

ΔT2 = 27000 - 8000

ΔT2 = 19000 cal

Therefore, the rise in temperature is 19000°C.