Question

Which of these statements describes this mathematical equation?

P1v1/t1=k

The final pressure of a gas is directly proportional to volume and temperature change.
The final pressure of a gas is directly proportional to volume change and Inversely proportional to temperature che
The final pressure of a gas is inversely proportional to the volume change and directly proportional to temperature
none of the above​

Answer 1

The final pressure of a gas is inversely proportional to the volume change and directly proportional to temperature

Step-by-step explanation:

Given

`(P_1V_1)/(T_1) = k`

Required

Interpret

`(P_1V_1)/(T_1) = k`

Multiply both sides by T1

`T_1 * (P_1V_1)/(T_1) = k * T_1`

`P_1V_1 = kT_1`

Divide both sides by V1

`(P_1V_1)/(V_1) = (kT_1)/(V_1)`

`P_1 = (kT_1)/(V_1)`

This can be rewritten as:

`P_1 = k(T_1)/(V_1)`

In the above expression; k is a constant of proportionality.

So, the equation can be written as variation as follows:

`P_1\ \alpha\ \ (T_1)/(V_1)`

To interpret:

P varies directly to T (the numerator) and inversely to V (the denominator).