Calculate the density of mercury (13.6 g’em’) in units of kg/m
The correct answer and explanation is :
To calculate the density of mercury in kg/m³, we start with the given value in g/cm³:
Given:
Density of mercury = 13.6 g/cm³
Step 1: Understand Unit Conversion
We are converting from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³).
Let’s break it down:
- 1 kilogram = 1,000 grams
- 1 meter = 100 centimeters
- So, 1 m³ = (100 cm)³ = 1,000,000 cm³
This gives us the conversion factor:
[
1 \text{ g/cm}^3 = \frac{1,000 \text{ g}}{1 \text{ kg}} \times \frac{1,000,000 \text{ cm}^3}{1 \text{ m}^3} = 1000 \text{ kg/m}^3
]
Step 2: Apply the Conversion
[
13.6 \text{ g/cm}^3 \times 1000 = 13,600 \text{ kg/m}^3
]
✅ Final Answer:
[
\boxed{13,600 \text{ kg/m}^3}
]
🔍 Explanation (300 words)
Density is a fundamental physical property defined as the mass per unit volume of a substance. It tells us how tightly matter is packed together in a given space. The SI unit of density is kilograms per cubic meter (kg/m³), while in laboratory settings, it is often expressed in grams per cubic centimeter (g/cm³).
In this problem, mercury’s density is given as 13.6 g/cm³, a relatively high value, reflecting its heaviness even in small volumes—this is why mercury feels much heavier than water for the same volume.
To convert between g/cm³ and kg/m³, we need to understand the relationship between the units:
- Since 1 kg = 1,000 g, and
- 1 m³ = 1,000,000 cm³,
we can conclude that: - 1 g/cm³ = 1,000 kg/m³
Thus, when we multiply the given density of mercury (13.6 g/cm³) by 1,000, we get 13,600 kg/m³.
This high density makes mercury useful in instruments like barometers and thermometers. Because it is so dense, even small volumes can exert noticeable pressure, making it ideal for measuring atmospheric pressure or temperature changes with precision.
Understanding unit conversion is critical in science and engineering, as different fields use different measurement systems. Converting correctly ensures accurate communication of data and avoids errors in calculation or design.