Answer: 12.55 C
Step-by-step explanation:
The relationship between gas volume and temperature is described by the Ideal Gas Law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
P1V1 = nRT1 (initial conditions)
P2V2 = nRT2 (final conditions)
Since the number of moles is constant, we can set nRT1 equal to nRT2:
P1V1 = P2V2
We can rearrange this equation to solve for the final temperature:
T2 = (P1V1/T1) * V2/P2
Substituting the given values:
T2 = (1 atm * 0.675 L / 308.15 K) * (0.635 L / 1 atm)
where we converted the initial temperature of 35 C to Kelvin by adding 273.15 K.
Simplifying and solving for T2:
T2 = 285.7 K - 273.15 K
T2 = 12.55 C
Therefore, the temperature of the room where the gas has a volume of 0.635 L at 1 atm is approximately 12.55 C.