A thin film of some solid material (with six degrees of freedom per atom) is dep

Question

A thin film of some solid material (with six degrees of freedom per atom) is deposited on a substrate of area 0.5 cm^2. The atomic spacing in the deposited material is 0.15 nm. Roughly what is the minimum thickness for this film if we want the relative fluctuations in its internal energy (sigma_E/E) to be less than a tenth of a part per billion? A canister containing, N_A nitrogen (N_2) molecules (where is Avogadro's number) is in thermal equilibrium with a large heat reservoir. Each molecule has three translational and two rotational degrees of freedom. Using nC_v = (Nv/2)k, find the number of degrees of freedom of the whole gas, the temperature of the reservoir, given that the mean energy of the gas is 3200 J. You want to bet that at any instant the internal energy of the gas is within x% of its mean value. What is the smallest percentage x that you could use here and still have at least a 68% chance of winning? A tiny bacterium has dimensions of about 10^-6 m in each direction. Assume that it is mostly water. How many molecules are in it? If each molecule has six degrees of freedom, what are the relative fluctuations in its temperature, sigma_T/T, given that nC_v = (Nv/2)k?

Explanation / Answer

ANS.

As a given probelm,

After solving the results would be ,

a) 3.35 *1010

b) 3.2 *10-6

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