To determine the most likely constants for the first row of the table given the equation [tex]\(P_1 V_1 = P_2 V_2\)[/tex], we need to recognize that this is an equation from Boyle's Law.
Boyle's Law states that for a given mass of gas at constant temperature, the product of pressure and volume is constant. The equation [tex]\(P_1 V_1 = P_2 V_2\)[/tex] describes how the pressure and volume of a gas change as long as the temperature and the amount of gas (number of moles) remain constant.
Let's break it down step-by-step:
1. Identify Boyle's Law:
[tex]\[ P_1 V_1 = P_2 V_2 \][/tex]
This is Boyle's Law.
2. Understand the implications of Boyle's Law:
Boyle's Law indicates that the product of pressure (P) and volume (V) remains constant if other factors (temperature, n - number of moles of gas) remain unchanged.
3. Determine the constants:
For [tex]\(P_1 V_1 = P_2 V_2\)[/tex] to hold true, the variables that might change (P, V) should be compensated by constants that do not (temperature, n).
4. Identify which variables are constant:
Since the equation holds true for constant temperature and the amount of gas, we recognize that these two must be our constants.
Thus, the appropriate constants to be filled in the first row of the table are "temperature and moles of gas."
So, the correct answer is:
temperature and moles of gas
