If 30cm3
of a gas at 50oC is warmed to 80oC at a
fixed pressure the fractional increase in volume is
A. 0.093
B. 1.090
C. 0.009
D. 0.910
To find the fractional increase in volume, we can use the formula:
fractional increase in volume = (final volume - initial volume) / initial volume
The initial volume is given as 30 cm^3.
To find the final volume, we can use the ideal gas law:
PV = nRT
Where:
P = pressure (which is given as fixed)
V = volume (initial and final)
n = number of moles (which remains constant as the gas is not changing)
R = gas constant
T = temperature (initial and final)
Since the pressure and number of moles remain constant, we can simplify the equation to:
V / T = constant
This means that the ratio of volume to temperature remains constant.
Let's call the final volume Vf and the final temperature Tf.
Vf / Tf = Vi / Ti
Vi is the initial volume (30 cm^3) and Ti is the initial temperature (50°C + 273 = 323 K).
We want to find the fractional increase in volume, which is:
(fractional increase in volume) = (Vf - Vi) / Vi
Rearranging the equation above, we can solve for Vf:
Vf = Vi * (Tf / Ti)
Substituting the given values:
Vf = 30 cm^3 * (353 K / 323 K)
Vf = 30 cm^3 * 1.0923
Vf ≈ 32.77 cm^3
Now we can calculate the fractional increase in volume:
(fractional increase in volume) = (32.77 cm^3 - 30 cm^3) / 30 cm^3
(fractional increase in volume) = 2.77 cm^3 / 30 cm^3
(fractional increase in volume) ≈ 0.0923
Therefore, the correct answer is approximately 0.092, which corresponds to option A.
To find the fractional increase in volume of a gas, we can use Charles's Law, which states that the volume of a given amount of gas is directly proportional to its absolute temperature, assuming constant pressure.
Let's denote the initial volume of the gas as V1 (30 cm^3) and the initial temperature as T1 (50 °C). Similarly, the final volume will be V2 and the final temperature will be T2 (80 °C).
First, let's convert the temperatures from Celsius to Kelvin by adding 273 to each value:
T1 = 50 °C + 273 = 323 K
T2 = 80 °C + 273 = 353 K
Now, we can use the formula for the fractional change in volume:
Fractional increase in volume = (V2 - V1) / V1
Using Charles's Law, we know that V2 / V1 = T2 / T1
Therefore, V2 = (T2 / T1) * V1
Plugging in the values, we get:
V2 = (353 K / 323 K) * 30 cm^3
V2 ≈ 32.794 cm^3
Now, we can calculate the fractional increase in volume:
Fractional increase in volume = (32.794 cm^3 - 30 cm^3) / 30 cm^3
Fractional increase in volume ≈ 0.093
Therefore, the correct answer is A. 0.093.