the heat of combustion of propane C3H8 2220 kj/mol the specific heat of copper is .385j/g C how many grams of propane. must be burned. to raise the temp. of a 10kg block of copper. from 25 C to 65C assuming. nonof the heat is lose of the surrounding
The Correct Answer and Explanation is :
To solve this problem, we need to determine how many grams of propane are required to raise the temperature of a 10 kg block of copper from 25°C to 65°C, assuming no heat is lost to the surroundings.
Step-by-step solution:
- Calculate the heat required to raise the temperature of the copper: The formula for heat is:
[
Q = mc\Delta T
]
where:
- ( Q ) is the heat absorbed (in joules),
- ( m ) is the mass of copper (in grams),
- ( c ) is the specific heat of copper (in joules per gram per degree Celsius),
- ( \Delta T ) is the change in temperature (in Celsius). Given:
- ( m = 10 \, \text{kg} = 10,000 \, \text{g} ),
- ( c = 0.385 \, \text{J/g°C} ),
- ( \Delta T = 65°C – 25°C = 40°C ). Substituting these values:
[
Q = (10,000 \, \text{g}) \times (0.385 \, \text{J/g°C}) \times (40°C)
]
[
Q = 154,000 \, \text{J}
] This is the amount of heat needed to raise the temperature of the copper block.
- Determine the amount of propane needed: The heat of combustion of propane is given as 2220 kJ/mol. We need to convert this value to joules:
[
2220 \, \text{kJ/mol} = 2,220,000 \, \text{J/mol}
] Now, we calculate how many moles of propane are needed to produce 154,000 J:
[
\text{Moles of propane} = \frac{\text{Heat required}}{\text{Heat of combustion per mole}} = \frac{154,000 \, \text{J}}{2,220,000 \, \text{J/mol}}
]
[
\text{Moles of propane} \approx 0.0694 \, \text{mol}
] - Convert moles of propane to grams: The molar mass of propane (C₃H₈) is:
[
3 \times 12 + 8 \times 1 = 44 \, \text{g/mol}
] Now, calculate the mass of propane required:
[
\text{Mass of propane} = 0.0694 \, \text{mol} \times 44 \, \text{g/mol}
]
[
\text{Mass of propane} \approx 3.05 \, \text{g}
]
Conclusion:
To raise the temperature of a 10 kg block of copper from 25°C to 65°C, approximately 3.05 grams of propane must be burned.
Let me now generate an image illustrating the calculation process.
Here is the educational diagram illustrating the calculation process for determining the grams of propane required to raise the temperature of the copper block. It shows the steps in a clear and simple manner.
