The universal gas law states that the volume ( V m^3) of a given mass of an ideal gas varies directly with its absolute temperature (TK) and inversely with its pressure (p N/m^2).
A certain mass of gas at an absolute temperature 285 K and pressure 10^5 N/m^2 has a volume 0.0235 m^3.
(a) Find the formula that connects p, V and T.
(b) hence find the pressure of the gas when its absolute temperature is 374 K and its volume is 0.018 m^3.
(a) According to the universal gas law, the formula connecting pressure (p), volume (V), and absolute temperature (T) is given by:
pV = kT
where k is a constant.
(b) To find the pressure of the gas when its absolute temperature is 374 K and its volume is 0.018 m^3, we can use the formula from part (a):
pV = kT
Since k is a constant, the equation can be rearranged as:
p = (kT) / V
To solve for p, we need to find the value of k. We can do this by using the given information:
V = 0.0235 m^3
T = 285 K
p = 10^5 N/m^2
We can substitute these values into the equation to solve for k:
10^5 * 0.0235 = k * 285
2350 = 285k
k = 2350 / 285
k ≈ 8.246
Now that we have the constant k, we can use it to find the pressure when T = 374 K and V = 0.018 m^3:
p = (8.246 * 374) / 0.018
p ≈ 171,753.333 N/m^2
Therefore, the pressure of the gas when its absolute temperature is 374 K and its volume is 0.018 m^3 is approximately 171,753.333 N/m^2.
(a) According to the given information and the universal gas law, we can express the relationship between pressure, volume, and temperature as:
V ∝ T / p
To remove the proportionality sign, we need to introduce a constant. Let's call this constant "k". So, the formula connecting p, V, and T can be written as:
V = k(T / p)
(b) To find the pressure when the temperature is 374 K and the volume is 0.018 m^3, we can use the formula derived above.
First, we need to determine the constant "k". We can do this by using the initial conditions provided. When the temperature is 285 K and the pressure is 10^5 N/m^2, the volume is 0.0235 m^3.
Plugging these values into the formula, we get:
0.0235 = k(285 / 10^5)
Simplifying this equation, we find:
k = 0.0235 * 10^5 / 285
k ≈ 821.93
Now that we have the value of "k", we can use it to find the pressure when the temperature is 374 K and the volume is 0.018 m^3.
Plugging these values into the formula, we get:
0.018 = 821.93(374 / p)
Rearranging the equation to solve for p, we have:
p = 821.93(374 / 0.018)
p ≈ 17,169,356 N/m^2
Therefore, the pressure of the gas when its absolute temperature is 374 K and its volume is 0.018 m^3 is approximately 17,169,356 N/m^2.