The correct form(s) of the formula for Charles's Law is (are): dot (V)_(1)T_(1)=V_(2)T_(2) (T_(1))/(T_(2))=(V_(1))/(V_(2)) V_(1)=T_(2)k (V)/(T)=k

Charles's Law describes how the volume of a gas changes with temperature, assuming that pressure and the amount of gas are held constant. The correct mathematical expression for Charles's Law is:<br /><br />\[<br />\frac{V}{T} = k<br />\]<br /><br />where \( V \) is the volume, \( T \) is the temperature in Kelvin, and \( k \) is a constant.<br /><br />Let's evaluate each given formula:<br /><br />1. \(\dot {V}_{1}T_{1}=V_{2}T_{2}\): This formula is incorrect. It does not correctly represent the relationship between volume and temperature in Charles's Law.<br /><br />2. \(\frac {T_{1}}{T_{2}}=\frac {V_{1}}{V_{2}}\): This formula is incorrect. The correct relationship should be \(\frac {V_{1}}{T_{1}} = \frac {V_{2}}{T_{2}}\).<br /><br />3. \(V_{1}=T_{2}k\): This formula is incorrect. It does not correctly express the proportionality between volume and temperature.<br /><br />4. \(\frac {V}{T}=k\): This formula is correct. It represents the direct proportionality between volume and temperature as described by Charles's Law.<br /><br />Therefore, the correct form of the formula for Charles's Law from the options provided is \(\frac{V}{T} = k\).