The volume of gas in a gas shock absorber varies inversely with the pressure and directly with the temperature. The volume is 24 cu. cm when the temperature is 30°C and the pressure is 25kg. What is the volume when the temperature is 20°C, and the pressure is 40 kg?
Well, let's break this down. We know that the volume of the gas is inversely proportional to the pressure and directly proportional to the temperature. So, we can use the formula:
V = k * (T/P)
where V is the volume, T is the temperature, P is the pressure, and k is the constant of proportionality.
Now, let's plug in the values we know: V = 24, T = 30, and P = 25. This gives us:
24 = k * (30/25)
Now, let's solve for k:
k = (24 * 25) / 30
k ≈ 20
So, the formula becomes:
V = 20 * (T/P)
Now, let's plug in the second set of values: T = 20 and P = 40. This gives us:
V = 20 * (20/40)
V = 20 * (1/2)
V = 10
Therefore, when the temperature is 20°C and the pressure is 40 kg, the volume of the gas in the shock absorber is 10 cubic centimeters.
And remember, it's not just about the answer, it's about the journey. Happy shock-absorbing!
To find the volume of gas in the shock absorber when the temperature is 20°C and the pressure is 40 kg, we can use the concept of inverse variation.
Let's denote the volume of gas as V, the temperature as T, and the pressure as P.
According to the given information, we have the following equations:
V ∝ 1/P (inversely proportional to pressure)
V ∝ T (directly proportional to temperature)
We can combine these equations to find the relationship between the volume, temperature, and pressure:
V = k(T/P)
where k is the constant of variation.
To find the value of k, we can use the initial conditions given in the problem. When T = 30°C and P = 25 kg, V = 24 cu. cm.
24 = k(30/25)
24 = k(6/5)
24 = (6/5)k
k = (5/6)(24) = 20
Now that we have the value of k, we can use it to find the volume when T = 20°C and P = 40 kg:
V = (20/40)(20)
V = (1/2)(20)
V = 10 cu. cm
Therefore, when the temperature is 20°C and the pressure is 40 kg, the volume of gas in the shock absorber is 10 cu. cm.
To find the volume of gas in the shock absorber when the temperature is 20°C and the pressure is 40 kg, we can use the equation that relates the volume, pressure, and temperature.
Let's break down the given information:
Volume₁ = 24 cu. cm
Temperature₁ = 30°C
Pressure₁ = 25 kg
We are asked to find the volume when:
Temperature₂ = 20°C
Pressure₂ = 40 kg
Now, let's use the inverse and direct variation concept to construct the equation.
Inversely Proportional: V ∝ 1/P (volume varies inversely with pressure)
Directly Proportional: V ∝ T (volume varies directly with temperature)
Combining these two variations, we get: V ∝ T/P
To find the constant of variation (k), we need to use the initial values:
Volume₁ = k * Temperature₁ / Pressure₁
Now, substitute the given values:
24 = k * 30 / 25
Simplify and solve for k:
24 * 25 = k * 30
k = (24 * 25) / 30
k = 20
Now that we have the constant of variation (k), we can use it to find the volume when the temperature is 20°C and the pressure is 40 kg.
Volume₂ = k * Temperature₂ / Pressure₂
Substituting the values:
Volume₂ = 20 * 20 / 40
Volume₂ = 10 cu. cm
Therefore, the volume of gas in the gas shock absorber when the temperature is 20°C and the pressure is 40 kg is 10 cubic centimeters.
first, pressure is in kPa or mg Hg, not kg.
V = kT/P
so
PV/T = k is constant
You want V such that
40V/(20+273) = 25*34/(30+273)