The volume of gas in a gas shock absorber varies inversely with the pressure and directly with the temperature. The volume is 24 cubic meters when the temperature is 30 degrees celsius and the pressure is 25 kg. What is the volume with the temperature is 20 degrees celsius and the pressure is 40 kg?
V = kT/P
so you want
x*40/20 = 24*25/30
unless you need the temperature in °K
To find the volume of the gas with a different temperature and pressure, we can use the concept of inverse variation and direct variation.
Inverse Variation: This means that if one variable increases, the other variable decreases by the same factor, and vice versa.
Direct Variation: This means that if one variable increases, the other variable also increases by the same factor, and vice versa.
In this case, the volume varies inversely with the pressure and directly with the temperature. So we can set up the following equation:
V ∝ T/P
where V represents the volume, T represents the temperature, and P represents the pressure.
Given that the volume is 24 cubic meters when the temperature is 30 degrees Celsius (T1 = 30) and the pressure is 25 kg (P1 = 25), we can substitute these values into the equation:
24 ∝ 30/25
Now, we can solve for the constant of proportionality (k) by multiplying both sides of the equation by 25:
24 * 25 = 30
600 = 30
k = 600/30
k = 20
Now that we have the value of k, we can use it to find the new volume (V2) when the temperature is 20 degrees Celsius (T2 = 20) and the pressure is 40 kg (P2 = 40):
V2 ∝ T2/P2
V2 = k * (T2/P2)
V2 = 20 * (20/40)
V2 = 20 * 0.5
V2 = 10
Therefore, the volume with a temperature of 20 degrees Celsius and a pressure of 40 kg is 10 cubic meters.