Recent content by GravityX

Hi, I had to calculate the entropy in a task of a lattice gas and derive a formula for the pressure from it and got the following $$P=\frac{k_b T}{a_0}\Bigl[ \ln(\frac{L}{a_0}-N(n-1)-\ln(\frac{L}{a_0}-nN) \Bigr]$$ But now I am supposed to calculate the following limit $$\lim\limits_{a_0...

Thanks vela for your help 👍 So ##\frac{3}{2}k_bT## instead of ##\frac{3}{2}RT##.

Thanks vela for your help I would now proceed as follows Translation:##\frac{3}{2}RT=\frac{\pi^2 \hbar^2}{2ML^2}(n_x^2+n_y^2+n_z^2)## Rotation: ##\frac{5}{2}RT=\frac{\pi^2 \hbar^2}{2ML^2}(n_x^2+n_y^2+n_z^2)+\frac{\hbar^2l(l+1)}{2\theta}## Oscillation: ##\frac{7}{2}RT=\frac{\pi^2...

Hi, I am unfortunately stuck with the following task I started once with the hint that at very low temperatures the diatomic ideal gas behaves like monatomic gas and has only three degrees of freedom of translation ##f=3##. If you then excite the gas by increasing the temperature, you add two...

Thank you Steve4Physics and haruspex for your help 👍, I had completely forgotten that the 0.4 was for the pair and not one base alone.

Unfortunately, I have problems with the following task For task 1, I proceeded as follows. Since the four bases have the same probability, this is ##P=\frac{1}{4}## I then simply used this probability in the formula for the Shannon entropy...

Thank you vanhees71 for your help and sorry I'm only getting back to you now, I had two weeks Christmas break 🎅 I was able to solve the problem now, the expression ##\Bigl\langle x_k\frac{\partial H }{\partial x_k} \Bigr\rangle## we had stated in the lecture as ##k_bT##.

The expression ##\langle \cal H \rangle_k## is the expected value of the canonical ensemble. The Hamiltonian is defined as follows, with the scaling ##\lambda## ##\lambda \cal H ## : ##\lambda H(x_1, ...,x_N)=H(\lambda^{a_1}x_1,....,\lambda^{a_N}x_N)## As a hint, I should differentiate the...

It is a 1D Tonk gas consisting of ##N## particles lined up on the interval ##L##. The particles themselves have the length ##a##. Between two particles there is a gap of length ##y_i##. ##L_f## is the free length, i.e. ##L_f=L-Na##. I have now received the following tip: Determine the...

I looked at the question again more closely, the task says "when expanding", so the force ensures that the folded segments are unfolded, for this they must be stretched by the length ##\lambda##, so the energy is thus $$\epsilon_{AF}=F\lambda$$ $$\epsilon_{BF}=\epsilon+F\lambda$$ Would this...

Hi It is about a DNA strand on which there are always two segments, the segment ##A##, which is folded and has the length ##l_A## and the unfolded segment ##B##, which has ##l_B+\lambda##. Here is a section of the DNA There is now, as shown in the picture, a force ##F## pulling on the...

Thanks Chestermiller for your help 👍 , your derivation also helped me with the second task :smile:

The task only says fluid (gas or liquid), so it is not explicitly mentioned. It then goes on to say The fluid is in equilibrium, homogeneous in temperature, and consists of one type of particle with mass m

Hi Unfortunately, I can't get on with the following task. The system looks like this it is divided in such a way that the same number of particles is present in each ##\epsilon## section. I am now to determine the energy ##E(P_h,V_h,N)## at the height h using the energy ##h=0## i.e...

Thanks Chestermiller for your help 👍 That would then mean that ##\kappa_T## would be curved to the left. If I have understood correctly, then ##\kappa_T## must always be positive for the system to be stable. The problem says "For which of the sketched isotherms does this pose a problem?" I...