Help my math pleaseplease

Mathematics

2 answers:

Alex Ar [27]2 years ago

6 0

Answer:

Answer below in picture.

I hope it helps.

polet [3.4K]2 years ago

5 0

Answer:

Volume is 135 cc when the temperature drops to 270K and the pressure is 150 N/cm²

Step-by-step explanation:

Given :

$\small\purple\bull$ Volume = 225 cc
$\small\purple\bull$ Temperature = 300K
$\small\purple\bull$ Pressure = 100 N/cm²

$\begin{gathered}\end{gathered}$

To Find :

$\small\purple\bull$ Volume when the temperature drops to 270K and the pressure is 150 N/cm²

$\begin{gathered}\end{gathered}$

Solution :

Mathematically, the relationship between the three variables is given by the expression :

$\longrightarrow{\sf{V = \dfrac{kT}{P}}}$

$\pink\star$ V = Volume
$\pink\star$ P = Pressure
$\pink\star$ T = Temperature
$\pink\star$ k = constant

$\rule{200}2$

Substituting all the given values in the formula to find k (constant)

$\begin{gathered}\qquad\longrightarrow{\sf{225= \dfrac{300k}{100}}}\\\\\qquad\longrightarrow{\sf{300k = 225 \times 100}}\\\\\qquad\longrightarrow{\sf{300k = 22500}}\\\\\qquad\longrightarrow{\sf{k = \dfrac{22500}{300}}}\\\\\qquad\longrightarrow{\sf{k = \dfrac{225 \: \cancel{00}}{3 \: \cancel{00}}}}\\\\\qquad\longrightarrow{\sf{k = \dfrac{225}{3}}}\\\\\qquad\longrightarrow{\sf{k = 75}}\end{gathered}$

Hence, the value of k is 75.

$\rule{200}2$

Now, finding the volume by substituting the values in the formula :

$\begin{gathered}\qquad\longrightarrow{\sf{V = \dfrac{kT}{P}}}\\\\\qquad\longrightarrow{\sf{V = \dfrac{75 \times 270}{150}}}\\\\\qquad\longrightarrow{\sf{V = \dfrac{20250}{150}}}\\\\\qquad\longrightarrow{\sf{V = \dfrac{2025 \: \cancel{0}}{15 \: \cancel{0}}}}\\\\\qquad\longrightarrow{\sf{V = \dfrac{2025}{15}}}\\\\\qquad\longrightarrow{\sf{V = 135 \: cc }}\end{gathered}$