A flight attendant wants to change the temperature of the air in the cabin from 18.0° C to 23.3° C without changing the number of moles of air per m3. What fractional change in pressure would be required?

P/T= constant or

P1/T1=P2/T2

or
T2/T1=P2/P1

I am not certain what you mean by fractional change, if it is P2/P1, you are done. Now if you mean as fractional change

(P2-P1)/P1 you have to subtract one from P2/P1

ie (P2-P1)/P1= P2/P1 - 1

i worked the problem out using that formula but i kept getting the wrong answer

(23.3-18)/18=0.294

To determine the fractional change in pressure required to change the temperature from 18.0°C to 23.3°C without changing the number of moles of air per m³, we can use the ideal gas law.

The ideal gas law is given by the formula:

PV = nRT

Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature in Kelvin

Since we want to find the fractional change in pressure, we can assume that the volume, number of moles, and gas constant remain constant. We are only changing the temperature.

To convert the given temperatures to Kelvin, we need to add 273.15 to each value:

T₁ = 18.0°C + 273.15 = 291.15 K
T₂ = 23.3°C + 273.15 = 296.45 K

Since we want to keep the number of moles of air per m³ constant, the value of n/V will remain constant. Therefore, we can write the equation as:

P₁/T₁ = P₂/T₂

Solving for the fractional change in pressure (P₂/P₁):

P₂/P₁ = (T₂/T₁)

Substituting the given values:

P₂/P₁ = (296.45 K / 291.15 K)

Calculating the fractional change in pressure:

P₂/P₁ ≈ 1.018

Therefore, the required fractional change in pressure to increase the temperature from 18.0°C to 23.3°C without changing the number of moles of air per m³ is approximately 1.018.