(Solved): problem 1,2 and 3 steps and theory please. Estimate the constant-volume specific heat capacity ...

problem 1,2 and 3
steps and theory please.

Estimate the constant-volume specific heat capacity $$C_V$$ of benzene $$\left({\mathrm{C}}_6{\mathrm{H}}_6\right)$$, in units of the ideal gas constant $$R$$. See the image of benzene structure below. Explain your estimate in detail. Recall that for a monatomic ideal gas, $$C_V=\frac{3}{2}R$$. Figure 1: Benzene molecule Problem 2 An interstellar gas cloud consists of atomic hydrogen with density $$n_{\mathrm{H}}=10^4{\mathrm{cm}}^{?3}$$. At what temperature would the thermal (kinetic) pressure of the gas be equal to the radiation pressure of the photons emitted by the gas? Problem 3 One kilomole of a monatomic ideal gas follows the reversible closed cycle shown in the figure below. Here, $$P_1=10\mathrm{atm},V_1=2{\mathrm{m}}^3$$, and $$V_2=4{\mathrm{m}}^3$$. The segment of the cycle from point 1 to point 2 is adiabatic. Calculate the change in entropy for each segment of the cycle. What is the sum of entropy changes over the complete cycle? Figure 2: Thermal cycle