Problem: A gas is compressed in a piston-cylinder system. Determine the work done on the gas during the compression process. Solution: The work done on the gas can be calculated using the equation W = P(V2 - V1), where P is the pressure and V2 and V1 are the final and initial volumes of the gas, respectively.

Problem: A heat engine operates between two reservoirs at temperatures T1 and T2. Calculate the efficiency of the heat engine. Solution: The efficiency of a heat engine can be calculated using the equation η = 1 - (T2 / T1), where T1 is the higher temperature and T2 is the lower temperature.

Problem: A refrigerator operates between two reservoirs at temperatures T1 and T2. Determine the coefficient of performance (COP) of the refrigerator. Solution: The coefficient of performance of a refrigerator can be calculated using the equation COP = Qc / W, where Qc is the heat removed from the cold reservoir and W is the work done on the refrigerator.

Problem: A gas undergoes an isothermal expansion. Calculate the change in entropy of the gas. Solution: The change in entropy of a gas undergoing an isothermal process can be calculated using the equation ΔS = nR ln(V2 / V1), where n is the number of moles of gas, R is the gas constant, and V2 and V1 are the final and initial volumes of the gas, respectively.

Problem: A system undergoes an adiabatic process. Determine the final temperature of the system. Solution: The final temperature of a system undergoing an adiabatic process can be calculated using the equation T2 = T1 (V1 / V2)^(γ-1), where T1 is the initial temperature, V1 and V2 are the initial and final volumes of the system, respectively, and γ is the heat capacity ratio.

Problem: A gas is heated at constant volume. Calculate the change in internal energy of the gas. Solution: The change in internal energy of a gas heated at constant volume can be calculated using the equation ΔU = nCvΔT, where n is the number of moles of gas, Cv is the molar specific heat at constant volume, and ΔT is the change in temperature.

Problem: A gas is heated at constant pressure. Determine the change in enthalpy of the gas. Solution: The change in enthalpy of a gas heated at constant pressure can be calculated using the equation ΔH = nCpΔT, where n is the number of moles of gas, Cp is the molar specific heat at constant pressure, and ΔT is the change in temperature.

Problem: A gas expands irreversibly against a constant external pressure. Calculate the work done by the gas. Solution: The work done by a gas expanding irreversibly against a constant external pressure can be calculated using the equation W = Pext(V2 - V1), where Pext is the external pressure and V2 and V1 are the final and initial volumes of the gas, respectively.

Problem: A heat pump transfers heat from a cold reservoir to a hot reservoir. Determine the coefficient of performance (COP) of the heat pump. Solution: The coefficient of performance of a heat pump can be calculated using the equation COP = Qh / W, where Qh is the heat transferred to the hot reservoir and W is the work done on the heat pump.

Problem: A gas undergoes a reversible isothermal process. Calculate the work done by the gas. Solution: The work done by a gas undergoing a reversible isothermal process can be calculated using the equation W = nRT ln(V2 / V1), where n is the number of moles of gas, R is the gas constant, and V2 and V1 are the final and initial volumes of the gas, respectively.

Problem: A system undergoes a polytropic process. Determine the equation of the process. Solution: The equation of a polytropic process can be determined using the equation PV^n = constant, where P is the pressure, V is the volume, and n is the polytropic index.

Problem: A gas is compressed adiabatically. Calculate the final temperature of the gas. Solution: The final temperature of a gas compressed adiabatically can be calculated using the equation T2 = T1 (V1 / V2)^(γ-1), where T1 is the initial temperature, V1 and V2 are the initial and final volumes of the gas, respectively, and γ is the heat capacity ratio.

Problem: A gas expands isobarically. Determine the work done by the gas. Solution: The work done by a gas expanding isobarically can be calculated using the equation W = P(V2 - V1), where P is the constant pressure and V2 and V1 are the final and initial volumes of the gas, respectively.

Problem: A system undergoes a reversible adiabatic process. Calculate the change in entropy of the system. Solution: The change in entropy of a system undergoing a reversible adiabatic process can be calculated using the equation ΔS = nCv ln(T2 / T1), where n is the number of moles of gas, Cv is the molar specific heat at constant volume, and T2 and T1 are the final and initial temperatures of the system, respectively.

Problem: A gas is heated at constant volume. Determine the change in enthalpy of the gas. Solution: The change in enthalpy of a gas heated at constant volume can be calculated using the equation ΔH = ΔU + PΔV, where ΔU is the change in internal energy, P is the pressure, and ΔV is the change in volume.