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Answer :
The correct temperature is C. 60.5°F and the mass is 1.07 x 10²kg.
Convert temperature:
- To convert Kelvin (K) to Fahrenheit (°F), use the formula: °F = (K - 273.15) x (9/5) + 32
- Plug in the temperature: °F = (289 K - 273.15) x (9/5) + 32 ≈ 60.5°F
Calculate mass:
- Density = mass / volume (given)
- Rearrange the formula to find mass: mass = density x volume
- Plug in the values: mass = 4.1 g/cm³ x 26,112 cm³ = 107,059.2 grams
Convert mass to kilograms:
- There are 1000 grams (g) in 1 kilogram (kg).
- Convert grams to kilograms: mass (kg) = mass (g) / 1000
- mass (kg) = 107,063.2 g / 1000 ≈ 1.07 x 10²kg (round to two significant digits).
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The conversion formula for Kelvin to Fahrenheit and the density formula were used to determine these values. Therefore, the correct answer is 60.5°F; 1.07 x 10² kg.
- The student asked: "An object at 289°K has a density of 4.1g/cm³ and a volume of 26,112cm³. Which answer choice represents BOTH the correct temperature of the object in Fahrenheit AND the correct mass of the object in kg.
First, let's convert the temperature from Kelvin to Fahrenheit. The formula to convert Kelvin to Fahrenheit is given by:
F = (K - 273.15) × 9/5 + 32
- (289 K - 273.15) = 15.85°C
- 15.85°C × 9/5 = 28.53°F
- 28.53°F + 32 = 60.53°F
The mass of the object can be calculated using the formula for density:
Density = Mass/Volume
Rearranging for mass:
Mass = Density × Volume
- Mass = 4.1 g/cm³ × 26,112 cm³
- Mass = 107,059.2 grams
- Convert grams to kilograms: 107,059.2 grams / 1000 = 107.0592 kilograms
The closest answer is 1.07 x 10² kg.
The correct answer is 60.5°F; 1.07 x 10²kg.
