Solve for P₁ (P_1V_1)/T_1=(P_2V_2)/T_2

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$

Step 1

Multiply both sides by $T_{1}$ .

$\frac{P_{1} V_{1}}{T_{1}} T_{1} = \frac{P_{2} V_{2}}{T_{2}} T_{1}$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $T_{1}$ .

Cancel the common factor.

$\frac{P_{1} V_{1}}{T_{1}} T_{1} = \frac{P_{2} V_{2}}{T_{2}} T_{1}$

Rewrite the expression.

$P_{1} V_{1} = \frac{P_{2} V_{2}}{T_{2}} T_{1}$

Simplify the right side.

Combine $\frac{P_{2} V_{2}}{T_{2}}$ and $T_{1}$ .

$P_{1} V_{1} = \frac{P_{2} V_{2} T_{1}}{T_{2}}$

Step 3

Divide each term in $P_{1} V_{1} = \frac{P_{2} V_{2} T_{1}}{T_{2}}$ by $V_{1}$ and simplify.

Divide each term in $P_{1} V_{1} = \frac{P_{2} V_{2} T_{1}}{T_{2}}$ by $V_{1}$ .

$\frac{P_{1} V_{1}}{V_{1}} = \frac{\frac{P_{2} V_{2} T_{1}}{T_{2}}}{V_{1}}$

Simplify the left side.

Cancel the common factor of $V_{1}$ .

Cancel the common factor.

$\frac{P_{1} V_{1}}{V_{1}} = \frac{\frac{P_{2} V_{2} T_{1}}{T_{2}}}{V_{1}}$

Divide $P_{1}$ by $1$ .

$P_{1} = \frac{\frac{P_{2} V_{2} T_{1}}{T_{2}}}{V_{1}}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$P_{1} = \frac{P_{2} V_{2} T_{1}}{T_{2}} \cdot \frac{1}{V_{1}}$

Multiply $\frac{P_{2} V_{2} T_{1}}{T_{2}}$ by $\frac{1}{V_{1}}$ .

$P_{1} = \frac{P_{2} V_{2} T_{1}}{T_{2} V_{1}}$