Thermodynamics and Ideal Gas
First Law-Exercise:
Problem 1: A volume 10 m3 contains 8 kg of oxygen at a temperature of 300 K. Find the work necessary to decrease the volume to 5 m3, (a) at a constant pressure and (b) at constant temperature. (c) What is the temperature at the end of the process in (a)? (d) What is the pressure at the end of process in (b)? (e) Show both processes in the p-V plane. Problem 2: The temperature of an ideal gas at an initial pressure p1 and volume V1 is increased at constant volume until the pressure is doubled. The gas is then expanded isothermally until the pressure drops to its original value, where it is compressed at constant pressure until the volume returns to its initial value. (a) Sketch these processes in the p-V plane and in the p-T plane. (b) Compute the work in each process and the net work done in the cycle if n = 2 kmoles, p1 = 2 atm and V1 = 4 m3. Problem 3: A 735 W stirring motor is applied to a tank of water. The tank contains 25 kg of water, and the stirring action is applied for 1 hour. Assuming that the tank is perfectly insulated, calculate the change in internal energy of the water. Also calculate the rise in temperature of the water, assuming that the process occurs at constant volume and that cv for water may be taken as 4.18 kJ/kg.K. Problem 4: A 0.0283 m3 container is filled with air at 1.365 bar and 37.77oC. Calculate the final pressure in the container if 10544.82 J of heat are added. Assume ideal gas behaviour, with constant specific heats. Problem 5: Nitrogen is to be heated at constant pressure from 310.77 K to 1921.88 K. Calculate the heat transfer per mole. C p 39.65
8071 1.5 106 kJ for N 2 T T 2 kg.K
Problem 6: Air is contained in a piston-cylinder arrangement with a cross sectional area of 4 cm2 and an initial volume of 20 cm3. The air is initially at 1 atm and 20oC. Connected to the piston is a spring having a deformation constant of ks = 100 N/cm and the spring is initially undeformed. How much heat
Problem 1: A volume 10 m3 contains 8 kg of oxygen at a temperature of 300 K. Find the work necessary to decrease the volume to 5 m3, (a) at a constant pressure and (b) at constant temperature. (c) What is the temperature at the end of the process in (a)? (d) What is the pressure at the end of process in (b)? (e) Show both processes in the p-V plane. Problem 2: The temperature of an ideal gas at an initial pressure p1 and volume V1 is increased at constant volume until the pressure is doubled. The gas is then expanded isothermally until the pressure drops to its original value, where it is compressed at constant pressure until the volume returns to its initial value. (a) Sketch these processes in the p-V plane and in the p-T plane. (b) Compute the work in each process and the net work done in the cycle if n = 2 kmoles, p1 = 2 atm and V1 = 4 m3. Problem 3: A 735 W stirring motor is applied to a tank of water. The tank contains 25 kg of water, and the stirring action is applied for 1 hour. Assuming that the tank is perfectly insulated, calculate the change in internal energy of the water. Also calculate the rise in temperature of the water, assuming that the process occurs at constant volume and that cv for water may be taken as 4.18 kJ/kg.K. Problem 4: A 0.0283 m3 container is filled with air at 1.365 bar and 37.77oC. Calculate the final pressure in the container if 10544.82 J of heat are added. Assume ideal gas behaviour, with constant specific heats. Problem 5: Nitrogen is to be heated at constant pressure from 310.77 K to 1921.88 K. Calculate the heat transfer per mole. C p 39.65
8071 1.5 106 kJ for N 2 T T 2 kg.K
Problem 6: Air is contained in a piston-cylinder arrangement with a cross sectional area of 4 cm2 and an initial volume of 20 cm3. The air is initially at 1 atm and 20oC. Connected to the piston is a spring having a deformation constant of ks = 100 N/cm and the spring is initially undeformed. How much heat