First law of thermodynamics and work done

[fly_bo1]

Two kilograms of water at 100oC is converted to steam at 1 ATM. Find the work done (in J). (The density of steam at 100oC is 0.598 kg/m3.)

a. 4.6 x 104
b. 3.4 x 104
c. 1.2 x 105
d. 2.1 x 104
e. 3.4 x 105

I'ved use the integration holding volume as a variable. However, I don't know why I am not getting the right answer.

 

[Andrew Mason]

Two kilograms of water at 100oC is converted to steam at 1 ATM. Find the work done (in J). (The density of steam at 100oC is 0.598 kg/m3.)

a. 4.6 x 104
b. 3.4 x 104
c. 1.2 x 105
d. 2.1 x 104
e. 3.4 x 105

I'ved use the integration holding volume as a variable. However, I don't know why I am not getting the right answer.

You don't have to do an integration. Assume that the change in volume from water to steam occurs at 1 Atm external pressure and that the steam is created gradually. Pressure is constant, so $W = \int PdV = PV$ (assume initial volume is 0).

AM

PS Welcome to PF, btw.

 

[nlightner]

I would like to provide a thorough response to this question. The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this scenario, the energy in the form of heat is being converted into work.

To calculate the work done, we need to use the formula W = PΔV, where W is the work done, P is the pressure, and ΔV is the change in volume. In this case, we know the pressure (1 ATM) and the change in volume (from liquid water to steam).

To find the change in volume, we can use the density of steam at 100oC, which is 0.598 kg/m3. Since we have 2 kg of water, the initial volume is 2 kg / 1000 kg/m3 = 0.002 m3. The final volume is the volume of the steam, which we can calculate using the density: V = m/ρ = 2 kg / 0.598 kg/m3 = 3.344 m3.

Plugging in these values into the formula, we get W = (1 ATM)(3.344 m3 - 0.002 m3) = 3.342 J. Therefore, the correct answer is b. 3.4 x 104 J.

It is possible that your method of using integration may have led to an incorrect answer. I would recommend double-checking your calculations and making sure you are using the correct formula for work done. Additionally, it is always helpful to have someone else review your work to catch any potential errors.