Later in the semester you will learn about the combined gas law which is expressed as PV, 1=22 where P is pressure, V is volume, and T is temperature. The subscripts 1 and 2 T represent the value of each of these variables at two different conditions. Rearrange this equation to solve for T2. P.V,

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### Combined Gas Law

Later in the semester, you will learn about the combined gas law, which is expressed as:

\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]

where \( P \) is pressure, \( V \) is volume, and \( T \) is temperature. The subscripts 1 and 2 represent the value of each of these variables at two different conditions. You will need to rearrange this equation to solve for \( T_2 \).

### Rearranging the Equation

To isolate \( T_2 \) in the combined gas law equation, follow these steps:

1. Cross-multiply the equation to eliminate the fractions:
   \[ P_1 V_1 \cdot T_2 = P_2 V_2 \cdot T_1 \]

2. Solve for \( T_2 \):
   \[ T_2 = \frac{P_2 V_2 \cdot T_1}{P_1 V_1} \]

This rearranged form allows you to solve for the temperature at the second condition (\(T_2\)) if you know the pressure, volume, and temperature at the first condition (\(P_1 V_1 T_1\)) and the pressure and volume at the second condition (\(P_2 V_2\)).
Transcribed Image Text:### Combined Gas Law Later in the semester, you will learn about the combined gas law, which is expressed as: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \] where \( P \) is pressure, \( V \) is volume, and \( T \) is temperature. The subscripts 1 and 2 represent the value of each of these variables at two different conditions. You will need to rearrange this equation to solve for \( T_2 \). ### Rearranging the Equation To isolate \( T_2 \) in the combined gas law equation, follow these steps: 1. Cross-multiply the equation to eliminate the fractions: \[ P_1 V_1 \cdot T_2 = P_2 V_2 \cdot T_1 \] 2. Solve for \( T_2 \): \[ T_2 = \frac{P_2 V_2 \cdot T_1}{P_1 V_1} \] This rearranged form allows you to solve for the temperature at the second condition (\(T_2\)) if you know the pressure, volume, and temperature at the first condition (\(P_1 V_1 T_1\)) and the pressure and volume at the second condition (\(P_2 V_2\)).
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