Question

question 6
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a metal block with a mass of 15 pounds is heated from an initial temperature of 70°f to a final temperature of 170°f. the specific heat capacity of the metal is 0.15 btu/lb°f. the change in the metal blocks thermal energy is equal to 3825 j.

Explanation:

Step1: Convert mass from pounds to kg

1 pound = 0.453592 kg, so 15 pounds = 15×0.453592 = 6.80388 kg

Step2: Convert temperatures from Fahrenheit to Celsius

The formula to convert Fahrenheit to Celsius is $C=\frac{5}{9}(F - 32)$. Initial temperature $T_1=\frac{5}{9}(70 - 32)=\frac{5}{9}\times38\approx21.11^{\circ}C$, final temperature $T_2=\frac{5}{9}(170 - 32)=\frac{5}{9}\times138\approx76.67^{\circ}C$. Temperature change $\Delta T=T_2 - T_1=76.67 - 21.11 = 55.56^{\circ}C$

Step3: Use the heat - energy formula

The formula for heat energy $Q = mc\Delta T$. Assume the specific heat capacity $c$ of the metal (not given in the problem - let's assume a value for illustration, say $c = 0.45\ J/(g\cdot^{\circ}C)=450\ J/(kg\cdot^{\circ}C)$). Then $Q=6.80388\times450\times55.56$
$Q = 6.80388\times450\times55.56=6.80388\times25002=170083.62\ J$

However, if we assume the problem has some standard values or we were supposed to work with given values in a different way, we need more information. But if we go by the general steps of solving for heat energy change:

Answer:

We need the specific heat capacity value to give an exact answer. If we assume $c = 450\ J/(kg\cdot^{\circ}C)$, the heat energy change is approximately 170084 J.