Let's analyze the given options to find which equation agrees with the ideal gas law.
The ideal gas law is expressed as:
[tex]\[ PV = nRT \][/tex]
where:
- [tex]\( P \)[/tex] is the pressure,
- [tex]\( V \)[/tex] is the volume,
- [tex]\( n \)[/tex] is the number of moles,
- [tex]\( R \)[/tex] is the universal gas constant,
- [tex]\( T \)[/tex] is the temperature in Kelvin.
When dealing with changes in the state of a gas, the combined gas law is often used. The combined gas law is derived from the ideal gas law and is given by:
[tex]\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \][/tex]
where subscript 1 denotes the initial state and subscript 2 denotes the final state.
Let's analyze the provided options:
1. [tex]\( \frac{V_i}{T_1} = \frac{V_2}{T_2} \)[/tex]
- This equation represents the relationship derived from the combined gas law but under the condition where the pressure is constant. If the pressure is constant, we can simplify the combined gas law by canceling out the pressure:
[tex]\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \][/tex]
- Hence, this option is correct under the condition of constant pressure.
2. [tex]\( OV.73=V272 \)[/tex]
- This equation does not match any known form of the ideal gas law or combined gas law. It seems to be an incorrect or malformed expression.
3. [tex]\( 0P9n1 = P2 / T2 \)[/tex]
- This equation does not match the format of the combined gas law or the ideal gas law. It is not recognizable as any valid gas law equation.
4. [tex]\( P2 T1 / P T2 \)[/tex]
- This expression is incomplete and does not align with any known gas law equations.
Based on this analysis, the equation that agrees with the ideal gas law, specifically under the condition of constant pressure, is:
[tex]\[ \frac{V_i}{T_1} = \frac{V_2}{T_2} \][/tex]
Therefore, the correct option is:
[tex]\[ \boxed{1} \][/tex]
