Homework 2. Due 1/28

1. Consider a cylinder filled with air with a piston and spring arrangement on top, as shown in the

figure below. The external pressure is 1 bar, the initial temperature of the air in the cylinder is 25 oC. The no-load length of the spring is 50 cm and the spring constant is 40,000 N/m. The piston

weighs 500 kg. You can assume the constant volume heat capacity of air to be constant at 20.3

J/(mol K).

a. Compute the initial pressure of the gas in the cylinder

b. Compute how much heat must be added to the gas in the cylinder to for the spring to

compress by 2 cm. You can treat the air as an ideal gas (15 pts)

2. Now consider the cylindrica

MPa. The pressure outside

rises to 0.6 MPa and the volume

(a) Sketch the path followed by the gas on a P

(b) Calculate the work done by the gas and the change in p

1

Consider a cylinder filled with air with a piston and spring arrangement on top, as shown in the

figure below. The external pressure is 1 bar, the initial temperature of the air in the cylinder is 25

load length of the spring is 50 cm and the spring constant is 40,000 N/m. The piston

weighs 500 kg. You can assume the constant volume heat capacity of air to be constant at 20.3

Compute the initial pressure of the gas in the cylinder (10 pts)

Compute how much heat must be added to the gas in the cylinder to for the spring to

compress by 2 cm. You can treat the air as an ideal gas (15 pts)

al piston assembly below which initially contains 0.2 m

e the piston is 0.1 MPa. The cylinder is heated till the gas p

the volume of the gas is 0.5 m3.

path followed by the gas on a P-V graph (5 pts)

he work done by the gas and the change in potential energy of the spring (

Consider a cylinder filled with air with a piston and spring arrangement on top, as shown in the

figure below. The external pressure is 1 bar, the initial temperature of the air in the cylinder is 25

load length of the spring is 50 cm and the spring constant is 40,000 N/m. The piston

weighs 500 kg. You can assume the constant volume heat capacity of air to be constant at 20.3

Compute how much heat must be added to the gas in the cylinder to for the spring to

initially contains 0.2 m3 of a gas at 0.3

The cylinder is heated till the gas pressure

otential energy of the spring (20 pts)

2

3. A polytropic process is a process that can be described by the empirical equation PVn = C, where

C is a constant which doesn’t depend on P or V. Consider the process where 20 Kg of air is

compressed from 1 bar, 300 K to 5 bar in a single stage compressor. If the process is polytropic

with n=1.25, determine:

(a) The work done by the compressor (12 pts)

(b) The amount of heat transferred to the surroundings (13 pts)

The specific heat of air at constant pressure in KJ/kmol K is Cp = 27.4528 + 6.1839 x 10-3

T –

8.9932 x 10-7

T2

4. Steam tables

a. Use the steam tables to determine the phase of water at the following conditions.

Explain why you made your choice. (10 pts)

i. 25 oC, 1 bar

ii. 200 oC, 10 bar

iii. 250 oC, 50 bar

b. A drum 3.5 m3 in volume contains steam at 1 bar, 210

oC. Determine the mass of the

steam in the drum. (15 pts)

4. (Honors option) The heat of vaporization (∆Qvap) is the amount of heat required to vaporize a

liquid (turn liquid into gas) at constant temperature and pressure. Since this process is at constant

pressure, ∆Qvap=∆Hvap .

a. Using steam tables, calculate ∆Hvap = Hvapor-Hliquid at 50 oC for 2 kg of water. (5 pts)

b. Using steam tables, find the saturated (equilibrium) vapor pressure of water @ 50 oC.

(The saturation vapor pressure of water is the partial pressure of water (Pwater = yP) when

the vapor is at equilibrium with the water) (4 pts)

c. Calculate the specific ∆hvap (at 1 bar) for methane if the intermolecular potential is given

by:

� = 4� �����− ���

�

With a = 2.05 x 10-21

J and σ = 3.72 angstroms. Assume that each molecule has twelve

neighbors (each molecule needs to be separated from twelve other molecules). The

specific volume of methane gas is 1.819 kg/m3 and of liquid methane it is 422.6 kg/m

3 at

1 bar and the boiling point. (15 pts)

Hint: calculate the work to pull the methane molecules apart from a separation distance of

21/6σ to infinity.

d. What is the measured value of ∆hvap ? Is it close to your value in (c)? (1 pt)