A calorimeter contains 100 gram of ice at -20 degree centigrade. X g of water at 80 degree centigrade is added to a calorimeter such that the final contents of the calorimeter are thermal in equilibrium with 40 degree centigrade of Mercury. The value of X is.?


To solve this problem, we need to use the principle of conservation of energy. The heat lost by hot water is equal to the heat gained by the ice and water in the calorimeter. The final temperature of the calorimeter is 40 degree centigrade, which means that the heat lost by the hot water is equal to the heat gained by the ice and water in the calorimeter.


We can use the following formula to calculate the heat lost by the hot water:

Q = m * c * delta T

where Q is the heat lost, m is the mass of water, c is the specific heat capacity of water, and delta T is the change in temperature.

We know that the heat lost by the hot water is equal to the heat gained by the ice and water in the calorimeter. Therefore, we can use the following formula to calculate the heat gained by the ice and water in the calorimeter:

Q = m * c * delta T

where Q is the heat gained, m is the mass of ice and water in the calorimeter, c is the specific heat capacity of ice and water, and delta T is the change in temperature.

We know that the final temperature of the calorimeter is 40 degree centigrade. Therefore, the change in temperature for both the hot water and the ice and water in the calorimeter is:

delta T = 80 - 40 = 40

Now, we can set the two equations equal to each other and solve for X:

X * 1 * (80 - 40) = (100 + X) * 2.1 * 40

Simplifying the equation, we get:

40X = 8400 + 84X

Subtracting 84X from both sides, we get:

-44X = 8400

Dividing both sides by -44, we get:

X = -190.91

Since the value of X cannot be negative, we can conclude that no water can be added to the calorimeter to achieve thermal equilibrium with 40 degree centigrade of Mercury.


In conclusion, the value of X cannot be determined as no water can be added to the calorimeter to achieve thermal equilibrium with 40 degree centigrade of Mercury.