Dry saturated steam at 100'C is passed into 250gm of a mixture of ice and water contained in a calorimeter of thermal capacity 45J/K.When all the ice has just melted,the mass of the content of the calorimeter has increased by 10gm due to condensed steam.Assuming no heat exchange between the calorimeter and its surroundings,calculate (a) the mass of ice initially in the calorimeter,and
(b) the rise in temperature when the passage of steam is continued until a further 15gm of steam has condensed and the mixture is in thermal equilibrium.Specific latent heat of vapourization of water is 2 260 000 J/kg and Specific heat capacity of water 4200J/Kg.K.
Please we need the answer urgently
To solve this problem, we can use the principle of energy conservation.
First, let's calculate the energy absorbed by the ice to melt it. The energy absorbed is equal to the mass of ice multiplied by the specific latent heat of fusion.
(a) Mass of ice initially in the calorimeter:
Let's assume the mass of ice initially in the calorimeter is m kg. Since the mass of ice has increased by 10 g (or 0.01 kg) after the steam condensed, the mass of ice initially in the calorimeter would be m - 0.01 kg.
The energy absorbed by the ice to melt is given by:
Energy absorbed = (mass of ice initially in the calorimeter) x (specific latent heat of fusion)
Energy absorbed = (m - 0.01 kg) x (2,260,000 J/kg)
Next, let's calculate the energy transferred to the water in the calorimeter to increase its temperature. The energy transferred to the water is given by the specific heat capacity of water multiplied by the change in temperature and the mass of the water.
(b) Rise in temperature when the passage of steam is continued:
Now, the total mass of the content in the calorimeter is the sum of the mass of ice initially in the calorimeter and the mass of water initially in the calorimeter, as well as the additional 15 g (or 0.015 kg) of condensed steam.
Total mass of the content in the calorimeter = (mass of ice initially in the calorimeter) + (mass of water initially in the calorimeter) + (mass of condensed steam)
The energy transferred to the water to increase its temperature is given by:
Energy transferred = (specific heat capacity of water) x (change in temperature) x (mass of water initially in the calorimeter + mass of condensed steam)
Energy transferred = (4200 J/kg.K) x (change in temperature) x (m kg + 0.015 kg)
According to the principle of energy conservation, the energy absorbed by the ice to melt is equal to the energy transferred to the water to increase its temperature. Therefore, we can equate the two expressions and solve for the change in temperature.
Energy absorbed = Energy transferred
(m - 0.01 kg) x (2,260,000 J/kg) = (4200 J/kg.K) x (change in temperature) x (m kg + 0.015 kg)
Now, you can solve these equations to find the values of (a) mass of ice initially in the calorimeter and (b) the rise in temperature when the passage of steam is continued until a further 15 g of steam has condensed and the mixture is in thermal equilibrium.