Question

1. during summer, concrete can have a range in temperature between 70 °f and 135 °f.

a. convert 70 °f to degrees celsius.
b. convert 135 °f to degrees celsius.
c. if one cubic meter of concrete has a mass of 2400 kg and a specific heat of 840 $j/(kg·°c)$. how much thermal energy is required to achieve the above temperature change.

Explanation:

Step1: Apply Fahrenheit to Celsius formula (part a)

The conversion formula is $C = \frac{5}{9}(F - 32)$. Substitute $F=70$:
$C = \frac{5}{9}(70 - 32) = \frac{5}{9} \times 38 \approx 21.11$

Step2: Apply Fahrenheit to Celsius formula (part b)

Use the same formula, substitute $F=135$:
$C = \frac{5}{9}(135 - 32) = \frac{5}{9} \times 103 \approx 57.22$

Step3: Calculate temperature change in °C

Find the difference between the two Celsius temperatures:
$\Delta T = 57.22 - 21.11 = 36.11 \, ^\circ\text{C}$

Step4: Calculate thermal energy (part c)

Use the heat formula $Q = mc\Delta T$, substitute $m=2400\ \text{kg}$, $c=840\ \frac{J}{kg \cdot ^\circ\text{C}}$, $\Delta T=36.11\ ^\circ\text{C}$:
$Q = 2400 \times 840 \times 36.11 = 2400 \times 30332.4 = 72797760$

Answer:

a. $21.11 \, ^\circ\text{C}$
b. $57.22 \, ^\circ\text{C}$
c. $72797760 \, \text{J}$ (or $7.28 \times 10^7 \, \text{J}$)