To determine which expressions are correct variations of the Combined Gas Law, let's recall the Combined Gas Law and review each expression step by step.
The Combined Gas Law states:
[tex]\[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
\][/tex]
We need to analyze each given expression to see if it can be derived correctly from the Combined Gas Law.
### Expression 1:
[tex]\[
T_1 = T_2 \left(\frac{P_1 V_1}{P_2 V_2}\right)
\][/tex]
Starting from the Combined Gas Law:
[tex]\[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
\][/tex]
Isolate [tex]\(T_1\)[/tex]:
[tex]\[
T_1 = T_2 \left(\frac{P_1 V_1}{P_2 V_2}\right)
\][/tex]
This expression is derived correctly from the Combined Gas Law.
### Expression 2:
[tex]\[
V_2 = V_1 \left(\frac{T_2}{T_1}\right) \left(\frac{P_1}{P_2}\right)
\][/tex]
Starting from the Combined Gas Law:
[tex]\[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
\][/tex]
Isolate [tex]\(V_2\)[/tex]:
[tex]\[
V_2 = \frac{P_1 V_1 T_2}{P_2 T_1}
\][/tex]
Which simplifies to:
[tex]\[
V_2 = V_1 \left(\frac{T_2}{T_1}\right) \left(\frac{P_1}{P_2}\right)
\][/tex]
This expression is also derived correctly from the Combined Gas Law.
### Conclusion
Both given expressions:
[tex]\[
T_1 = T_2 \left(\frac{P_1 V_1}{P_2 V_2}\right)
\][/tex]
and
[tex]\[
V_2 = V_1 \left(\frac{T_2}{T_1}\right) \left(\frac{P_1}{P_2}\right)
\][/tex]
are correct variations of the Combined Gas Law.
