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5gm of ice at 0 degree celsius is mixed with 10 gm of steam at 100 degree Celsius. Find the final temperature and the composition of mixture if the mixing is done in a calorimeter of water equivalent 13 gm , initially at 0 degree Celsius?
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5gm of ice at 0 degree celsius is mixed with 10 gm of steam at 100 deg...
Solution:
To find the final temperature and composition of the mixture, we can use the principle of conservation of heat.
Step 1: Calculate the heat gained or lost by each component
First, let's calculate the heat gained or lost by ice, steam, and the calorimeter separately.
1. Heat gained or lost by ice:
The heat gained or lost by ice can be calculated using the formula:
Q = m * s * ΔT
Where,
Q = heat gained or lost (in calories)
m = mass of the substance (in grams)
s = specific heat capacity of the substance (in calories/gram °C)
ΔT = change in temperature (in °C)
Given that the mass of ice (m1) is 5 gm and the initial temperature (T1) is 0°C, the final temperature (Tf1) is unknown.
Using the specific heat capacity of ice (s1) as 0.5 cal/gm °C, we can calculate the heat gained or lost by ice (Q1):
Q1 = m1 * s1 * (Tf1 - T1)
2. Heat gained or lost by steam:
The heat gained or lost by steam can be calculated using the same formula as above. Given that the mass of steam (m2) is 10 gm and the initial temperature (T2) is 100°C, the final temperature (Tf2) is unknown.
Using the specific heat capacity of steam (s2) as 0.5 cal/gm °C, we can calculate the heat gained or lost by steam (Q2):
Q2 = m2 * s2 * (Tf2 - T2)
3. Heat gained or lost by the calorimeter:
The heat gained or lost by the calorimeter can be calculated using the same formula as above. Given that the water equivalent of the calorimeter (m3) is 13 gm and the initial temperature (T3) is 0°C, the final temperature (Tf3) is unknown.
Using the specific heat capacity of water (s3) as 1 cal/gm °C, we can calculate the heat gained or lost by the calorimeter (Q3):
Q3 = m3 * s3 * (Tf3 - T3)
Step 2: Apply the principle of conservation of heat
According to the principle of conservation of heat, the heat gained by one component is equal to the heat lost by the other components in an isolated system.
Since the ice, steam, and calorimeter are in an isolated system, we can write the equation as:
Q1 + Q2 = -Q3
Step 3: Solve the equation to find the final temperature
Substituting the values of Q1, Q2, and Q3 in the equation, we get:
m1 * s1 * (Tf1 - T1) + m2 * s2 * (Tf2 - T2) = -m3 * s3 * (Tf3 - T3)
Substituting the known values, we get:
5 * 0.5 * (Tf1 - 0) + 10 * 0.5 * (Tf2 - 100) = -13 * 1 * (Tf3 - 0)
S
To find the final temperature and composition of the mixture, we can use the principle of conservation of heat.
Step 1: Calculate the heat gained or lost by each component
First, let's calculate the heat gained or lost by ice, steam, and the calorimeter separately.
1. Heat gained or lost by ice:
The heat gained or lost by ice can be calculated using the formula:
Q = m * s * ΔT
Where,
Q = heat gained or lost (in calories)
m = mass of the substance (in grams)
s = specific heat capacity of the substance (in calories/gram °C)
ΔT = change in temperature (in °C)
Given that the mass of ice (m1) is 5 gm and the initial temperature (T1) is 0°C, the final temperature (Tf1) is unknown.
Using the specific heat capacity of ice (s1) as 0.5 cal/gm °C, we can calculate the heat gained or lost by ice (Q1):
Q1 = m1 * s1 * (Tf1 - T1)
2. Heat gained or lost by steam:
The heat gained or lost by steam can be calculated using the same formula as above. Given that the mass of steam (m2) is 10 gm and the initial temperature (T2) is 100°C, the final temperature (Tf2) is unknown.
Using the specific heat capacity of steam (s2) as 0.5 cal/gm °C, we can calculate the heat gained or lost by steam (Q2):
Q2 = m2 * s2 * (Tf2 - T2)
3. Heat gained or lost by the calorimeter:
The heat gained or lost by the calorimeter can be calculated using the same formula as above. Given that the water equivalent of the calorimeter (m3) is 13 gm and the initial temperature (T3) is 0°C, the final temperature (Tf3) is unknown.
Using the specific heat capacity of water (s3) as 1 cal/gm °C, we can calculate the heat gained or lost by the calorimeter (Q3):
Q3 = m3 * s3 * (Tf3 - T3)
Step 2: Apply the principle of conservation of heat
According to the principle of conservation of heat, the heat gained by one component is equal to the heat lost by the other components in an isolated system.
Since the ice, steam, and calorimeter are in an isolated system, we can write the equation as:
Q1 + Q2 = -Q3
Step 3: Solve the equation to find the final temperature
Substituting the values of Q1, Q2, and Q3 in the equation, we get:
m1 * s1 * (Tf1 - T1) + m2 * s2 * (Tf2 - T2) = -m3 * s3 * (Tf3 - T3)
Substituting the known values, we get:
5 * 0.5 * (Tf1 - 0) + 10 * 0.5 * (Tf2 - 100) = -13 * 1 * (Tf3 - 0)
S
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5gm of ice at 0 degree celsius is mixed with 10 gm of steam at 100 degree Celsius. Find the final temperature and the composition of mixture if the mixing is done in a calorimeter of water equivalent 13 gm , initially at 0 degree Celsius?
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5gm of ice at 0 degree celsius is mixed with 10 gm of steam at 100 degree Celsius. Find the final temperature and the composition of mixture if the mixing is done in a calorimeter of water equivalent 13 gm , initially at 0 degree Celsius? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 5gm of ice at 0 degree celsius is mixed with 10 gm of steam at 100 degree Celsius. Find the final temperature and the composition of mixture if the mixing is done in a calorimeter of water equivalent 13 gm , initially at 0 degree Celsius? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 5gm of ice at 0 degree celsius is mixed with 10 gm of steam at 100 degree Celsius. Find the final temperature and the composition of mixture if the mixing is done in a calorimeter of water equivalent 13 gm , initially at 0 degree Celsius?.
5gm of ice at 0 degree celsius is mixed with 10 gm of steam at 100 degree Celsius. Find the final temperature and the composition of mixture if the mixing is done in a calorimeter of water equivalent 13 gm , initially at 0 degree Celsius? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 5gm of ice at 0 degree celsius is mixed with 10 gm of steam at 100 degree Celsius. Find the final temperature and the composition of mixture if the mixing is done in a calorimeter of water equivalent 13 gm , initially at 0 degree Celsius? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 5gm of ice at 0 degree celsius is mixed with 10 gm of steam at 100 degree Celsius. Find the final temperature and the composition of mixture if the mixing is done in a calorimeter of water equivalent 13 gm , initially at 0 degree Celsius?.
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