A fixed mass of a perfect gas undergoes the following three processes: An expansion at constant temperature from a pressure and volume of 11 bar and $0.005\ \mathrm{m^3}$ respectively to a volume of $0.012\ \mathrm{m^3}$. Cooling at constant pressure until the volume is $0.007\ \mathrm{m^3}$. Constant volume heating until the gas reaches its original pressure of 11 bar. Determine the unknown pressure and temperature at the end of each process given that the initial temperature is $250^\circ\mathrm{C}$.

A gas power plant operates a gas turbine, which is modelled as an ideal Brayton cycle. At the compressor inlet, a mixture of natural gas and air is drawn in at a pressure of 5 bar at $32^\circ\mathrm{C}$. After combustion, the temperature of the gas reaches $3500^\circ\mathrm{C}$. You may assume that the working fluid is an ideal gas, with $R_g = 0.301\ \mathrm{kJ/kg/K}$ and $\gamma = 1.42$. Determine the required pressure ratio if the specific heat addition is 1800 kJ/kg. What is the resulting thermal efficiency and work ratio ($c_p = \dfrac{\gamma R_g}{\gamma - 1}$, $\eta_T = 1 - \dfrac{1}{r_p^{(\gamma-1)/\gamma}} = 1 - \dfrac{T_1}{T_2}$, $r_p$ is the pressure ratio, work ratio $r_w = \dfrac{w_{net}}{w_{out}} = 1 - \dfrac{T_1}{T_3} r_p^{(\gamma-1)/\gamma}$)

A house use sensible heat of concrete plate to realize self-heating. Given the size of the plate as $5\ \mathrm{m} \times 8\ \mathrm{m} \times 0.3\ \mathrm{m}$, the density as $2300\ \mathrm{kg/m^3}$, heat capacity as $0.65\ \mathrm{kJ/(kg\cdot K)}$. Please calculate the entropy production if the concrete plate decrease its temperature from $28^\circ\mathrm{C}$ to $18^\circ\mathrm{C}$ in the evening (ambient temperature $t_0 = 18^\circ\mathrm{C}$)