Two Fairly Basic Thermodynamics Questions

[jimmypoopins]

Please help! I need these done by wednesday and for the life of me i cannot seem to get the correct answer.

Homework Statement

How much ice must melt at 0 deg. C to gain 5 g of mass?

Homework Equations

I cannot seem to find many equations that relate thermodynamics and mass, maybe that is my biggest problem... The only one i could find was
Q=Lm

The Attempt at a Solution

I know the latent heat of fusion, but i do not know Q. I tried dividing both sides by L, giving me Q/L=m, but i wasn't sure where to go from there.

Homework Statement

Calculate the entropy change in isotermal transformation of ideal gas at the temperature of 27.5 deg. C if work done by the gas is 3.5 J.

Homework Equations

s(b)-s(a)=Cv*ln(Tb/Ta)+nR*ln(Vb/Va)
pV=nRT
dW=pdV

The Attempt at a Solution

since Tb/Ta=1, Cv*ln(Tb/Ta) is reduced to zero, leaving us with
s(b)-s(a)=nR*ln(Vb/Va)
i then attempted to use the ideal gas law combined with dW=pdV but i found myself running in circles trying to figure out what to do with p and n and trying to find Vb and Va at the same time.

 

[jimmypoopins]

anyone? please this is very important and it is due at 12:00 midnight. I've tried really hard and i will continue to try but if anyone can set me in the right direction i will greatly appreciate it

 

[m2003]

As a scientist, it is important to first understand the concepts and principles behind the equations being used. In the first question, you are correct in using the equation Q = Lm, where Q is the heat gained or lost, L is the latent heat of fusion, and m is the mass. In this case, we are looking for the mass, so we can rearrange the equation to solve for m: m = Q/L.

Now, we know that the ice is melting at 0 degrees Celsius, which means it is undergoing a phase change from a solid to a liquid. During this process, the temperature remains constant, but energy is being added to the system in the form of heat. Therefore, we can use the specific latent heat of fusion for water at 0 degrees Celsius, which is 334 J/g. Plugging this into our equation, we get: m = 5 g / (334 J/g) = 0.015 g of ice must melt to gain 5 g of mass.

For the second question, we are looking for the entropy change in an isothermal transformation of an ideal gas. The equation you have listed is correct, but it is important to understand what each variable represents. Cv is the specific heat capacity at constant volume, which for an ideal gas is (3/2)R, where R is the gas constant. n is the number of moles of gas, T is the temperature, and V is the volume.

Since the process is isothermal, the temperature remains constant, so the first term in the equation becomes 0. Now, we can use the ideal gas law to relate the volume and number of moles of gas: V = nRT/P, where P is the pressure. We also know that work done (dW) is equal to the change in pressure (dP) times the change in volume (dV): dW = dPdV.

Substituting these values into the equation, we get: s(b) - s(a) = (3/2)R*ln(Pb/Pa) + nR*ln(Vb/Va). Since the process is isothermal, we can assume that Pb/Pa = Vb/Va, so the second term becomes 0. Therefore, the final equation becomes: s(b) - s(a) = (3/2)R*ln(Pb/Pa).

To solve for the