# Carnot cycle use

1. Jan 9, 2016

### RingNebula57

I saw a problem for which I don't really understand the idea of the solution. This is what it says:
The vaporization latent heat for water (at 100 deg C) under normal pressure (101325 pa) is 2,3*10^6. What is the saturated vapor pressure for water at 105 deg C?
And the solution says that we have to consider a Carnot cycle in which the isotherms are at 100 deg C and 105 deg C, and the adiabats transform the water from water to vapor and vice-versa. And so ,expressing the efficency for the Carnot cyle as W/Q=1-T1/T2, where T1=100 deg C and T2=105 deg C , and saying that Q=(Mass of vapour)* ( latent heat of vaporization) and W=(delta)p*(delta)V, where (delta) V is the volume of the vapour and approximately equat to (m*R*T2)/(molar mass of water) form the ideal gas law , we can obtain (delta)p ,and then the final pressure P final= (delta)p + p, where p is the normal atmospheric pressure.

I am not stuck with the calcultion of this problem. I just don't understant why do we have to think of a Carnot cycle in a situation like this. When do we have to look at a system like at a Carnot cycle?

Thank you!

2. Jan 9, 2016

### Staff: Mentor

Someone figured out that, for this particular kind of problem, the Carnot cycle could be used as a "vehicle" for determining the effect of temperature on the equilibrium vapor pressure of a material. It is really a cute idea. This is not the way that the effect of temperature on equilibrium vapor pressure is usually determined in Thermo courses (i.e., the so-called Clausius Clapeyron equation).

Chet