An aluminum block of mass 12.00 kg is heated from 20 C to 118 C. If the specific heat of aluminum is $913 J-1 kg K -1$ then how much energy is required?
A. 1073.688 kJ
B. 64.640 kJ
C. 7456.167 kJ
D. 10.956 kJ
Answer (2)
Identify the given values: mass m = 12.00 kg, specific heat c = 913 J k g − 1 K − 1 , and temperature change Δ T = 98 K.
Apply the formula Q = m c Δ T to calculate the heat energy required.
Substitute the values: Q = ( 12.00 k g ) × ( 913 J k g − 1 K − 1 ) × ( 98 K ) = 1073688 J .
Convert Joules to kiloJoules: Q k J = 1000 1073688 J = 1073.688 k J . The final answer is 1073.688 k J .
Explanation
Problem Introduction We are given an aluminum block with a mass of 12.00 kg that is heated from 20 C to 118 C. The specific heat of aluminum is 913 J k g − 1 K − 1 . We need to find the amount of energy required for this process.
Stating the Formula To find the energy required, we use the formula: Q = m c Δ T where:
Q is the heat energy required (in Joules).
m is the mass of the aluminum block (in kg).
c is the specific heat of aluminum ( J k g − 1 K − 1 ).
Δ T is the change in temperature (in K or C).
Substituting the Values We have:
m = 12.00 kg
c = 913 J k g − 1 K − 1
Δ T = 118 C − 20 C = 98 C = 98 K Substituting these values into the formula, we get: Q = ( 12.00 k g ) × ( 913 J k g − 1 K − 1 ) × ( 98 K ) Q = 1073688 J
Converting to kJ Now, we convert the energy from Joules to kiloJoules by dividing by 1000: Q k J = 1000 1073688 J = 1073.688 k J
Final Answer Therefore, the energy required to heat the aluminum block is 1073.688 kJ.
Examples
This calculation is crucial in various engineering applications, such as designing heat exchangers or determining the energy consumption of heating elements. For instance, when designing a solar water heater, engineers need to calculate the amount of energy required to raise the water temperature to a desired level. By knowing the mass of the water, the specific heat capacity, and the desired temperature change, they can accurately determine the necessary energy input. This ensures the system is efficient and meets the required heating demands, optimizing both performance and cost.
The energy required to heat a 12.00 kg aluminum block from 20 °C to 118 °C is 1073.688 kJ, calculated using the specific heat capacity formula. Therefore, the correct answer is A. 1073.688 kJ.
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