ChBE 2100 - Spring 2026
Homework Set 8
Due: March 20 (Friday), 11:59 pm
Problem 1
A piston-fitted cylinder with a 6 cm inner diameter contains 1.40 g of nitrogen. The mass of the
piston is 4.50 kg, and a 25.00 kg weight rests on the piston. The gas temperature is 30°C, and the
pressure outside the cylinder is 2.50 atm.
a) The absolute pressure of the gas in the cylinder is 3.55 × 105 Pa. Calculate the volume
occupied by the gas, assuming ideal-gas behavior.
b) Suppose the weight is abruptly lifted and the piston rises to a new equilibrium position.
Further suppose that the process takes place in two steps: a rapid step in which a negligible
amount of heat is exchanged with the surroundings, followed by a slow step in which the
gas returns to 30°C. Considering the gas as the system, write the energy balances for step
1, step 2, and the overall process. In all cases, neglect ΔEk and ΔEp.
Problem 2
Air is heated from 25°C to 140°C prior to entering a combustion furnace. The change in specific
enthalpy associated with this transition is 3349 J/mol. The flow rate of air at the heater outlet is
1.65 m3/min and the air pressure at this point is 122 kPa absolute.
Calculate the heat requirement in kW, assuming ideal-gas behavior and that kinetic and potential
energy changes from the heater inlet to the outlet are negligible.
ChBE 2100 - Spring 2026
Homework Set 8
Problem 3
A fuel oil is burned with air in a boiler furnace. The combustion produces 528.45 kW of thermal
energy, which is all transferred as heat to boiler tubes that pass through the furnace. The
combustion products pass from the furnace to a stack at 550°C. Water enters the boiler tubes as a
liquid at 30°C and leaves the tubes as saturated steam at 20 bar absolute.
a) Calculate the rate (kg/hr) at which steam is produced.
b) Use the steam tables to estimate the volumetric flow rate of the steam produced.
Problem 4
During a period of relative inactivity, the total average rate of enthalpy change in the body is
approximately ΔH = −300 kJ/hr. Heat is transferred from the body to its surroundings at a rate
given by
Q̇ = hA(Ts – T0)
where A is the body surface area (roughly 1.8 m2 for an adult), Ts is the skin temperature (normally
34.2°C), T0 is the temperature of the body surroundings, and h is a heat transfer coefficient. Typical
values of h for the human body are:
h = 8 kJ/(m2 hr °C) (fully clothed; slight breeze blowing)
h = 64 kJ/(m2 hr °C) (nude; immersed in water)
a) Consider the human body as a continuous system at steady state. Write an energy balance
on the body, making all appropriate simplifications and substitutions.
b) Calculate the surrounding temperature for which the energy balance is satisfied (i.e., at
which a person would feel neither hot nor cold) for a clothed person and for a nude person
immersed in water.
Reminder:
- Start early.
- Reach out to classmates and work together, just make sure to write your own answer.
- Other ways to get help: post a question on Piazza, go to office hours, etc.
- You will get a zero for the entire HW if you copy solution manual or copy each other.
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