Why is a vacuum tube called a valve in electronics?

The correct relation for a triode is

The amplification factor of a triode is $18$ and its plate resistance is $8 \times 10^{3} \ \Omega$. $A$ load resistance of $10^{4} \ \Omega$ is connected in the plate circuit. The voltage gain will be

The voltage gain of a triode depends upon

In a diode valve,the cathode temperature must be ($\phi$ = work function):

The plate current in a triode is given by ${I_p} = 0.004 ({V_p} + 10{V_g})^{3/2} \text{ mA}$,where ${I_p}, {V_p}$ and ${V_g}$ are the values of plate current,plate voltage,and grid voltage,respectively. What are the triode parameters $\mu$,${r_p}$ and ${g_m}$ for the operating point at ${V_p} = 120 \text{ V}$ and ${V_g} = -2 \text{ V}$?