Question

Consider a mole of an ideal monatomic gas, Xe, inside a container with rigid walls. The ideal gas is heated up as a flame is applied to the container’s exterior. The molar mass of Xe is 0.131 kg. The gas does not transfer any heat to the container. Answer the following questions.

A.) Before the flame is lit, the pressure of the gas inside the container is 10.1x10^5 Pa and the temperature of the gas is 295 K. If at some time later the pressure is measured to be 20.2x10^5 Pa, what is the volume of the gas?

B.) What is the temperature of the gas at this time?

C.) If at some time later the temperature is measured to be 425 K, by how much did the internal energy of the gas increase?

D.)In (c), how much heat was transferred to the gas?

(d) What is the heat capacity of the gas?

Answer 1

A) Since the container has rigid walls, its volume does not change. Hence final volume = initial volume = nRT/P =(1*8.314*295)/(10.1*10^5) = 0.002428 m3.

B) Since process is isochoric(constant volume), P1/T1 = P2/T2

T2 = (P2/P1)T1 = (20.2*10^5)/(10.1*10^5)*295 = 590 K

C) Cv for monoatomic gas = 12.47 J/mol-K

ΔU = nCvΔT = 1*12.47*(425-295) = 1621.23 J

D) By First Law, ΔQ = ΔU + ΔW. Since process is ischoric, ΔW = 0. Hence, ΔQ = ΔU = 1621.23 J. Heat capacity = Cv = 12.47 J/mol-K