Constant-volume gas thermometer

[Rblswimmer456]

Homework Statement

The pressure in a constant-volume gas ther-
mometer is 0.811 atm at 100◦C and 0.5 atm
at 0◦C.

A) What is the temperature when the pressure
is 0.656922 atm?
Answer in units of ◦C.

B) What is the pressure at 138◦C?
Answer in units of atm.

Homework Equations

well I know that P1/T1=P2/T2 but I don't know how to go about it since two pressure and temperatures are given so I don't know the formula to find the third.

for part B I figured I would have to get part A before attempting the second part.

The Attempt at a Solution

 

[rock.freak667]

They gave you the pressures at two temperatures. You can use either one as P1 and T1.

I mean P1 and the corresponding T1 that is.

 

[Dadface]

I think the main problem is that the gas differs from ideal behaviour and by a substantial amount.Using the given data P/T is nowhere near constant.

 

[rock.freak667]

Then it is likely that some sort of linear relationship should be found using the two points.

 

[rwisz]

I can provide a response to this content by using the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and inversely proportional to its volume. In a constant-volume gas thermometer, the volume remains constant, so we can use the ideal gas law to calculate the temperature at a given pressure.

A) To find the temperature when the pressure is 0.656922 atm, we can rearrange the ideal gas law to solve for temperature: T = (P1V1)/P2. Plugging in the given values, we get T = (0.811 atm * V1)/(0.656922 atm). Since the volume is constant, we can cancel it out, and we are left with T = 1.2349 * 100◦C. Therefore, the temperature is 123.49◦C.

B) Now, to find the pressure at 138◦C, we can use the same equation and rearrange it to solve for pressure: P2 = (P1V1)/T2. Plugging in the given values, we get P2 = (0.5 atm * V1)/(138◦C). Again, since the volume is constant, we can cancel it out, and we are left with P2 = 0.003623 atm. Therefore, the pressure at 138◦C is 0.003623 atm.