To find the width of the sides of the aluminum cube, we'll need to use the information provided and convert the units as necessary. Here's how you can do it step by step:
1. Convert the temperature from Fahrenheit to Celsius:
- Initial temperature: 62°F = (62 - 32) × 5/9 = 16.67°C
- Final temperature: 149°F = (149 - 32) × 5/9 = 65°C
2. Calculate the temperature change (∆T) in Celsius:
∆T = Final temperature - Initial temperature
∆T = 65°C - 16.67°C = 48.33°C
3. Convert the heat absorbed from calories to joules:
- Given heat = 16.2 calories
- 1 calorie = 4.184 joules
- Heat in joules = 16.2 calories × 4.184 joules/calorie
4. Calculate the mass (m) of the aluminum cube:
- Density (ρ) = 2.99 g/cm^3
- Volume (V) of a cube = (side length)^3
- Convert density to kg/m^3: 2.99 g/cm^3 = 2990 kg/m^3
- Volume (V) = (side length)^3 = (side length)^3 cm^3
- Side length = (Volume)^(1/3) cm
- Side length = [(16.2 calories × 4.184 joules/calorie) / (0.22 cal/g°C × 48.33°C)]^(1/3) cm
5. Convert side length to inches:
1 inch = 2.54 cm
Side length in inches = Side length in cm / 2.54
Now, you have all the steps required to calculate the width of the sides of the aluminum cube. I'll let you do the necessary calculations using the given values.