The volume V of a fixed amount of a gas varies directly as the temperature T and inversely, as the pressure P. Suppose that V = 160 cm^3 when T = 320 kelvin and p=12 kg/cm^2 find the temperature when v=90cm^3 and p=16 kg/cm^2
First, let's write the direct and inverse proportionality equation for the volume V:
V = k * T / P
Where k is the constant of variation.
Now we can use the initial conditions to find the value of k:
160 = k * 320 / 12
k = 160 * 12 / 320
k = 6
Now we can write the equation for V in terms of T and P:
V = 6 * T / P
Next, substitute the new values of V and P to find the temperature T:
90 = 6 * T / 16
90 * 16 = 6T
1440 = 6T
T = 1440 / 6
T = 240 kelvin
Therefore, the temperature when V=90cm^3 and P=16 kg/cm^2 is 240 kelvin.