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Answer :
Sure! Let's break down the solution for each part of the question step by step:
### a. Molar Heat Capacity of Water
1. Specific Heat of Water: The specific heat of water is 4.18 J/g°C. This means it takes 4.18 joules of energy to raise the temperature of 1 gram of water by 1°C.
2. Molar Mass of Water: The molar mass of water (H₂O) is approximately 18.015 g/mol. This means one mole of water weighs 18.015 grams.
3. Molar Heat Capacity Calculation: To find the molar heat capacity, multiply the specific heat by the molar mass:
[tex]\[
\text{Molar Heat Capacity} = 4.18 \, \text{J/g°C} \times 18.015 \, \text{g/mol} = 75.3027 \, \text{J/mol°C}
\][/tex]
This tells us how many joules it takes to raise the temperature of one mole of water by 1°C.
### b. Heat Capacity of 185g Water
1. Mass of Water: You have 185 grams of water.
2. Heat Capacity Calculation: To find the heat capacity, multiply the specific heat by the mass of the water:
[tex]\[
\text{Heat Capacity} = 4.18 \, \text{J/g°C} \times 185 \, \text{g} = 773.3 \, \text{J/°C}
\][/tex]
This tells us how many joules are needed to raise the temperature of 185 grams of water by 1°C.
### c. Heat Required to Raise Temperature of 10kg Water by 20°C
1. Mass of Water: Convert the mass from kilograms to grams since the specific heat is given in J/g°C. So, 10 kilograms is 10,000 grams.
2. Temperature Change: The temperature needs to be raised by 20°C.
3. Heat Required Calculation: Use the formula:
[tex]\[
\text{Heat Required} = \text{Specific Heat} \times \text{Mass} \times \text{Temperature Change}
\][/tex]
Substituting in the values:
[tex]\[
\text{Heat Required} = 4.18 \, \text{J/g°C} \times 10,000 \, \text{g} \times 20 \, \text{°C} = 836,000 \, \text{J}
\][/tex]
4. Conversion to kJ: Since 1 kJ = 1000 J, convert joules to kilojoules:
[tex]\[
\text{Heat Required in kJ} = \frac{836,000 \, \text{J}}{1000} = 836.0 \, \text{kJ}
\][/tex]
This tells us the amount of heat in kilojoules required to raise the temperature of 10 kilograms of water by 20°C.
I hope this detailed explanation helps you understand the concepts and calculations!
### a. Molar Heat Capacity of Water
1. Specific Heat of Water: The specific heat of water is 4.18 J/g°C. This means it takes 4.18 joules of energy to raise the temperature of 1 gram of water by 1°C.
2. Molar Mass of Water: The molar mass of water (H₂O) is approximately 18.015 g/mol. This means one mole of water weighs 18.015 grams.
3. Molar Heat Capacity Calculation: To find the molar heat capacity, multiply the specific heat by the molar mass:
[tex]\[
\text{Molar Heat Capacity} = 4.18 \, \text{J/g°C} \times 18.015 \, \text{g/mol} = 75.3027 \, \text{J/mol°C}
\][/tex]
This tells us how many joules it takes to raise the temperature of one mole of water by 1°C.
### b. Heat Capacity of 185g Water
1. Mass of Water: You have 185 grams of water.
2. Heat Capacity Calculation: To find the heat capacity, multiply the specific heat by the mass of the water:
[tex]\[
\text{Heat Capacity} = 4.18 \, \text{J/g°C} \times 185 \, \text{g} = 773.3 \, \text{J/°C}
\][/tex]
This tells us how many joules are needed to raise the temperature of 185 grams of water by 1°C.
### c. Heat Required to Raise Temperature of 10kg Water by 20°C
1. Mass of Water: Convert the mass from kilograms to grams since the specific heat is given in J/g°C. So, 10 kilograms is 10,000 grams.
2. Temperature Change: The temperature needs to be raised by 20°C.
3. Heat Required Calculation: Use the formula:
[tex]\[
\text{Heat Required} = \text{Specific Heat} \times \text{Mass} \times \text{Temperature Change}
\][/tex]
Substituting in the values:
[tex]\[
\text{Heat Required} = 4.18 \, \text{J/g°C} \times 10,000 \, \text{g} \times 20 \, \text{°C} = 836,000 \, \text{J}
\][/tex]
4. Conversion to kJ: Since 1 kJ = 1000 J, convert joules to kilojoules:
[tex]\[
\text{Heat Required in kJ} = \frac{836,000 \, \text{J}}{1000} = 836.0 \, \text{kJ}
\][/tex]
This tells us the amount of heat in kilojoules required to raise the temperature of 10 kilograms of water by 20°C.
I hope this detailed explanation helps you understand the concepts and calculations!
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