An insulated piston-cylinder device initially contains 300 L of air at 120 kPa and 17 oC. Air is now heated for 15 min by a 200-w resistance heater placed inside the cylinder. The pressure of air is maintained constant during this process. Determine the entropy change of air assuming (a) ) constant specific heats and (b) ) variable specific heats.

a)  

b)  

Explanation:

a)

Specific heat formula, we have:

Where

m is mass

c is specific heat capacity of air at specific temp

is the temperature change

W is the power

t is the time

The ideal gas law is:

Where

P is the pressure

V is the volume

n is number of moles

T is temperature

R is the ideal gas constant

First, lets solve for in the 1st equation, remembering to use ideal gas law in it to have the variables that are given in the problem. Shown below:

Now, we know

Theta_1 is 17 celsius, which in Kelvin is 17 + 270 = 290K

Power is 200

Time is 15 mins = 15 * 60 = 900 seconds

R is 287 J/kg K

P is 120

V is 300 L

Specific heat of air at 290K is about 1005

Substituting we get:

Now, Entropy Change is:

Again using the substitution equations, we have:

We know what the variables mean, we substitute the respective values, to get:

b)

For variable specific heats, we need entropy value from entropy table:

s_2 = 2.58044

s_1 = 1.66802  [1.05 * 290 K]

The formula is:

Substituting the values, we find the