Water of mass 200g and temperature 10digrees Celsius is put in a copper calorimeter of mass 80g. Steam from boiler at a normal pressure is passed into the calorimeter for sometime. The total mass of the calorimeter and contents is 283g. The final temperature of the contents is measured and is T.
Determine:
(i) heat lost by the steam on condensing to water.
(ii) heat lost by condensed water.
(iii) heat gained by the calorimet rer and the cold water.
(iv) the value of T.
(i) heat lost on condensing is Q = mL
=3X2.26X10^3Joules = 6780 Joules
(iv) 0.383X80X(T-10) + 4.186X200X(T-10) = 6780 + 3X4.186X(100-T)
Solve for T
(ii) put the value of T in 2nd term of RHS in the above equation
(iii) Find the Value of LHS by substituting the value of T in the above equation
To solve this problem, we need to use the principles of calorimetry and the specific heat capacities of water and copper. Let's go through each step to find the values.
(i) Heat lost by the steam on condensing to water:
When steam condenses, it releases heat to its surroundings. To calculate the heat lost by the steam, we use the formula:
Q = m × L
Where:
Q = Heat lost
m = Mass of water formed (in this case, the mass of steam)
L = Latent heat of vaporization
The latent heat of vaporization (L) for water is 2260 J/g.
We need to find the mass of steam. We are given the mass of the water (200 g), the mass of the calorimeter (80 g), and the total mass of the system after steam is added (283 g).
The mass of steam can be calculated as follows:
Mass of steam = Total mass - (Mass of water + Mass of calorimeter)
Mass of steam = 283 g - (200 g + 80 g) = 3 g
Now we can calculate the heat lost:
Q = 3 g × 2260 J/g = 6780 J
So, the heat lost by the steam on condensing to water is 6780 J.
(ii) Heat lost by condensed water:
The heat lost by the condensed water can be calculated using the formula:
Q = m × c × ΔT
Where:
Q = Heat lost
m = Mass of water
c = Specific heat capacity of water
ΔT = Change in temperature
We are given the mass of water (200 g) and the initial temperature (10 degrees Celsius). We need to find the change in temperature (ΔT).
To find ΔT, we use the equation:
ΔT = T - initial temperature
(iii) Heat gained by the calorimeter and cold water:
The heat gained by the calorimeter and cold water can be calculated using the same formula as in part (ii):
Q = m × c × ΔT
In this case, the mass (m) is the sum of the mass of water (200 g) and the mass of the calorimeter (80 g). We need to find ΔT.
(iv) The value of T:
The final temperature (T) can be found by taking the average of the temperatures before and after the heat exchange:
T = (initial temperature + final temperature) / 2
By substituting the values, we can find the final temperature (T).
So, to summarize:
(i) Heat lost by the steam on condensing to water = 6780 J
(ii) Heat lost by condensed water = m × c × ΔT (calculate using water's specific heat capacity and ΔT)
(iii) Heat gained by the calorimeter and cold water = m × c × ΔT (calculate using copper's specific heat capacity and ΔT)
(iv) The value of T = (initial temperature + final temperature) / 2 (adjusting for ΔT calculations)