Sample Problems (Gaskell, 2003) – First Law of Thermodynamics

Sample Problem 1One mole of a monatomic ideal gas, in the initial state T=273K, P=1atm, is subjected to the following two processes, each of which is conducted reversibly:a. A doubling of its volume at constant pressure;b. Then a doubling of its pressure at constant volume.

Calculate the heat and work effects which occur during each of the processes.Cp=5R/2

Sample Problem 2An ideal gas at 300 K has a volume of 15 liters at a pressure of 15 atm. Calculate:

(1) the final volume of the system;(2) the work done by the system;(3) heat entering or leaving the system;(4) the change in the internal energy; and (5) the change in the enthalpy

when the gas undergoes a reversible adiabatic expansion to a pressure of 10 atm. The constant volume molar heat capacity of the gas (Cv) has the value of 3R/2.

Sample Problem 3Ten moles of ideal gas, in the initial state P1= 10atm, T1=300K, are taken round the following cycle:a. A reversible change of state along a straight line path on the P-V diagram to the

state, P=1atm, T-300K.b. A reversible isobaric compression to V=24.6L, andc. A reversible constant volume process to P=10atm.Draw the cycle path on a P-V diagram. Monitor the change in heat, work, and internal energy in each process. Express all values in kJ. Cv =3R/2

Problems for independent work

Problem 1 (Gaskell, 1973)A system comprises one mole of an ideal gas at 0ºC and 1 atm. The system is subjected to the following processes, each of which is conducted reversibly:

a. A 10-fold increase in volume at constant temperatureb. Then a 100-fold adiabatic increase in pressurec. Then a return to the initial state along a straight-line path in the P-V diagram.

Calculate the work done by the system in step c and the total heat added to or withdrawn from the system as a result of the cyclic process.

Problem 2 (Gaskell, 2003)

One mole of an ideal gas at 25ºC and 1 atm undergoes the following reversibly conducted process:

a. Isothermal expansion to 0.5 atm, followed byb. Isobaric expansion to 100ºC, followed byc. Isothermal compression to 1 atm, followed byd. Isobaric compression to 25ºC

The system then undergoes the following reversible cyclic process:a. Isobaric expansion to 100ºC, followed byb. A decrease in pressure at constant volume to P atm, followed byc. An isobaric compression at P atm to 24.5 liters, followed byd. An increase in pressure at constant volume to 1 atm

Calculate the value of P which makes the work done on the gas in the first cycle equal to the work done by the gas in the second cycle.

Problem 3 (Gaskell, 2003)Two moles of an ideal gas, in an initial state P = 10 atm, V = 5 liters, are taken reversible in a clockwise direction around a circular path given by (V-10)2 + (P-10)2 = 25. Calculate the amount of work done by the gas as a result of the process, and calculate the maximum and minimum temperatures attained by the gas during the cycle.

Problem 4 (Young et al, 2004) “A Thermodynamic Process in a Liquid”A chemical engineer is studying the properties of liquid methanol (CH3OH). She uses a steel cylinder with a cross-sectional area of 0.0200 m2 and containing 1.20 x 10-2 m3 of methanol. The cylinder is equipped with a tightly fitting piston that supports a load of 3.00 x 104 N. The temperature of the system is increased from 20.0ºC to 50.0ºC. For methanol, the coefficient of volume expansion is 1.20 x 10-3 K-1, the density is 791 kg/m3, and the specific heat capacity at constant pressure is cp = 2.51 x 103 J/kg-K. You can ignore the expansion of the steel cylinder. Find a). the increase in volume of the methanol;b). the mechanical work done by the methanol against the 3.00 x 104 N force;c). the amount of heat added to the methanol;d). the change in internal energy of the methanol.e). Based on your results, explain whether there is any substantial difference between the specific heat capacities cp (at constant pressure) and cv (at constant volume) for methanol under these conditions.