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## Main Question or Discussion Point

What do textbooks mean when the gas laws are "combined" to make the ideal gas law?

I think that if the equations were combined, the result would look something like this:

P = k(T)T P = k(V)/V P = k(n)n

P^3 = (k(T)T * k(V)*k(n)n)/V

or

P/T = k(T) PV = k(V) P/n = k(n)

(P^3*V)/nT = k(T)*K(V)*K(n)

(k(n), k(T), k(V) = constants)

I get pressure raised to the third power instead of plain pressure. Any pointers or insights into what I am not understanding? I find it hard to believe the very top three equations can just be mushed together without multiplying their respective pressures to get pressure to the third, as what PV = nRT suggests in my mind.

I think that if the equations were combined, the result would look something like this:

P = k(T)T P = k(V)/V P = k(n)n

P^3 = (k(T)T * k(V)*k(n)n)/V

or

P/T = k(T) PV = k(V) P/n = k(n)

(P^3*V)/nT = k(T)*K(V)*K(n)

(k(n), k(T), k(V) = constants)

I get pressure raised to the third power instead of plain pressure. Any pointers or insights into what I am not understanding? I find it hard to believe the very top three equations can just be mushed together without multiplying their respective pressures to get pressure to the third, as what PV = nRT suggests in my mind.