Question

In former times, gas volume was used as a way to measure temperature, using devices called gas thermometers. Consider a gas that has a volume of 0.675 L at 35 C and at 1 atm pressure. What is the temperature (in C)) of a room where the gas has a volume of 0.635 L at 1 atm?

Answer 1

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.