# Solving Density ρ Question: Δρ = -87x10-6ρ at 25ºC to -40ºC

• A_Munk3y
In summary, the change in density of a substance with a change in temperature is given by Δρ = −βρ ΔT, where β is a constant specific to the substance. To find the fractional change in density of a lead sphere with a temperature decrease from 25°C to −40º C, we can use the equation Δρ = −87x10-6ρ and divide it by the initial density of the lead sphere. This gives us a fractional change in density of 176.8, indicating a significant increase in density with a decrease in temperature.
A_Munk3y

## Homework Statement

Show that the change in the density ρ of a substance, when the temperature changes by ΔT,
is given by Δρ = −βρ ΔT. (b) What is the fractional change in density of a lead sphere whose
temperature decreases from 25°C to −40º C?

## The Attempt at a Solution

ok i already go the first part, but i don't think I am doing b right.

im just plugging in (-40-25) for temperature, and the β of lead.
so Δρ = −87x10-6ρ
ρ=176.8Δρ

i doubt that's the answer. am i misunderstanding the question here? or am i just doing something completely wrong?

A_Munk3y said:
ρ=176.8Δρ

This is right, but the question asks for fractional change in density. That means the change in density divided by the density itself.

oh... ok
thank you :)

## What is density?

Density is a physical property of matter that measures the mass of a substance per unit volume. It is often represented by the Greek letter ρ (rho).

## What is the equation for solving density?

The equation for density is ρ = m/V, where ρ is density, m is mass, and V is volume.

## What does the given equation Δρ = -87x10-6ρ at 25ºC to -40ºC mean?

This equation represents a change in density (Δρ) from 25ºC to -40ºC, where the change is equal to -87x10-6 times the original density (ρ) at 25ºC.

## How can this equation be used in scientific research?

This equation can be used to calculate the change in density of a substance at different temperatures, which can provide valuable information for various scientific studies and experiments.

## What units are used to measure density?

Density can be measured in a variety of units, including grams per cubic centimeter (g/cm3), kilograms per cubic meter (kg/m3), and pounds per cubic inch (lb/in3).

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