The universal gas law states that the volume(v m cube) of a given mass of an ideal gas varies directly with its absolute temperature (TK) and inversely with its absolute temperature (TK) and inversely with its temperature(TK) and inversely with its pressure (p N/m square ).
A certain mass of a gas at an absolute temperature 275k and pressure 10 raise to the power of 5 N/m square has a volume 0.0225 m raise to the power of 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 raise to the power of 3.
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A good reply
To find the formula that connects pressure (p), volume (v), and absolute temperature (T), we can start by analyzing the statement "the volume (v) of a given mass of an ideal gas varies directly with its absolute temperature (T) and inversely with its pressure (p)."
We can express this relationship using a proportionality constant. Let's call this constant "k":
v ∝ T/p
To remove the proportionality sign, we introduce an equality sign and substitute k with R (the ideal gas constant):
v = R * (T/p)
Now, let's solve part (a) of the question:
(a) Find the formula that connects p, v, and T.
The formula is v = R * (T/p), where R is the ideal gas constant (a constant value) and T is the absolute temperature measured in Kelvin.
Now, let's move on to part (b) of the question:
(b) Find the pressure of the gas when its absolute temperature is 374 K and its volume is 0.018 m^3.
To find the pressure, we can rearrange the formula from part (a) to solve for p:
p = R * (T/v)
Substituting the given values:
p = R * (374 K / 0.018 m^3)
To obtain the pressure, we need to know the value of the ideal gas constant (R), which depends on the units used for pressure, volume, and temperature. The most common value of R is 8.314 J/(mol·K).
However, since the given values do not include the number of moles of the gas, we cannot directly calculate the pressure using the ideal gas constant. We need additional information such as the identity of the gas or its molar mass to determine the number of moles, and subsequently, the pressure.
Therefore, without the molar mass or the identity of the gas, we cannot determine the exact pressure when the volume is 0.018 m^3 and the temperature is 374 K.
v = kT/P
So,
0.0225 = k*275/10^5
Now you can find k, and then answer the questions