In a particular engine a gas is compressed in the initial stroke of the piston. Measurements of the instantaneous temperature, carried out during the compression, reveal that the temperature increases according to the relation: T= (V/Vo)nTo where To and Vo are the initial temperature and volume and n is a constant. The gas is compressed to the volume V1 (where V1 < Vo). Assume that the gas is a monatomic ideal gas of N atoms, and assume the process is quasi-static (i.e. the system is always instantaneously in equilibrium). a) Calculate the mechanical work done on the gas. b) Calculate the change in the total energy of the gas. c) Calculate the heat transfer Q to the gas. For what value of n is Q = 0? Show that this corresponds to the case of adiabatic compression (see Problem lf). [Hint: you may use the facts you know about an ideal gas, i.e. pV=NKBT, and E = (3/2)NKBT.]

In a particular engine a gas is compressed in the initial stroke of the piston. Measurements of the instantaneous temperature, carried out during the compression, reveal that the temperature increases according to the relation: T= (V/Vo)nTo where To and Vo are the initial temperature and volume and n is a constant. The gas is compressed to the volume V1 (where V1 < Vo). Assume that the gas is a monatomic ideal gas of N atoms, and assume the process is quasi-static (i.e. the system is always instantaneously in equilibrium). a) Calculate the mechanical work done on the gas. b) Calculate the change in the total energy of the gas. c) Calculate the heat transfer Q to the gas. For what value of n is Q = 0? Show that this corresponds to the case of adiabatic compression (see Problem lf). [Hint: you may use the facts you know about an ideal gas, i.e. pV=NKBT, and E = (3/2)NKBT.]