Question

Rearrange the variable in the combined gas law to solve for $T_2$.

Short answer

The combined gas law for $T_2$ is role="math" localid="1652612034505" $T_2=\frac{T_1\times P_2\times V_2}{P_1\times V_1}$.

Step-by-step solution

Given Information

We need to rearrange the variable in combined gas law to solve for $T_2$

Simplify

The combined gas law is given as:

$\frac{P_1\times V_1}{T_1}=\frac{P_2\times V_2}{T_2}$

Here,

$P_1$is initial pressure,

$T_2$is initial temperature,

role="math" localid="1652611570206" $V_1$is initial volume,

$P_2$ is final pressure,

role="math" localid="1652611612307" $T_2$is final temperature and

$V_2$ is the final volume.

Now, in case if are asked to find the final temperature the combined gas equation will be rearranged as:

$$\begin{gathered} \frac{P_1\times V_1}{T_1}=\frac{P_2\times V_2}{T_2} \\ {T}_2\times P_1\times V_1=T_1\times P_2\times V_2 \end{gathered}$$

For $T_2$is equal to:

$T_2=\frac{T_1\times P_2\times V_2}{P_1\times V_1}$