Question

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

Answer 1

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.