5 pounds of an ideal gas with R=38.7 and K=1.668 have 300Btu of heat added during a reversible constant pressure change of state, initial temperature=80°F.

Determine:
a.)the final temperature
b.)change of internal energy
change of enthalpy
change of entropy

a) Since it is a constant pressure heating, dQ = M Cp dT = [K*M*R/((K-1)]*dT

Use that to determine the temperature changle dT, and add that to 80 F.

You need to specify the units of R. They should be Btu/lbm*degF

b) dU = M Cv dT = [M/(K-1)]dT
c) dH = Cp*dT = dQ
d) dS = Integral of dQ/T
= Integral of M Cp dT/T
= M Cp ln(T2/T1)
The T's must be in degrees Rankine

To determine the final temperature, change of internal energy, change of enthalpy, and change of entropy, we can use the following formulas:

a) The final temperature can be found using the ideal gas law equation:

PV = nRT

Where:
P is the pressure (constant pressure change of state)
V is the volume (not given, but assumed to be constant)
n is the number of moles (can be calculated using the given mass of the gas and its molar mass)
R is the specific gas constant (given as 38.7 for the ideal gas)
T is the temperature

Rearranging the equation to solve for T:

T = PV / (nR)

We need to convert the given pressure from lb/in² to lb/ft²:

1 lb/in² = 144 lb/ft²

b) Change of internal energy (ΔU) can be calculated using the equation:

ΔU = Q - W

Where:
Q is the heat added to the system (given as 300 Btu)
W is the work done by the system (can be calculated using the equation W = PΔV)

c) Change of enthalpy (ΔH) can be calculated using the equation:

ΔH = Q + PΔV

d) Change of entropy (ΔS) can be calculated using the equation:

ΔS = Q / T

Now, let's calculate each of these values.

First, we need to convert the mass of the gas from pounds to moles using the molar mass (M):

Molar mass = M = Molar mass of gas / 1 lb
= Molar mass of gas / 5 lb

Assuming you have the molar mass of the gas, substitute it into the equation to find the number of moles (n).

Now, let's calculate each component:

a) Final temperature:
Convert the given initial temperature from Fahrenheit to Rankine (R):
T₁ = 80°F + 460

Using the ideal gas equation:
T₂ = P * V / (n * R)

Substitute the given pressure, volume (assumed to be constant), number of moles (calculated above), and the specific gas constant (given as 38.7) to find the final temperature (T₂).

b) Change of internal energy:
Calculate the work done by the system (W) using the equation:
W = P * ΔV

Assuming the volume is constant, ΔV = 0, so W = 0.

Therefore,
ΔU = Q - W
= Q

Substitute the given heat added to the system (Q) to find the change of internal energy (ΔU).

c) Change of enthalpy:
ΔH = Q + PΔV

Since ΔV = 0 (assuming constant volume), ΔH = Q

Substitute the given heat added to the system (Q) to find the change of enthalpy (ΔH).

d) Change of entropy:
ΔS = Q / T

Substitute the given heat added to the system (Q) and the final temperature (T₂) to find the change of entropy (ΔS).

By following these steps, you should be able to calculate the final temperature (a), change of internal energy (b), change of enthalpy (c), and change of entropy (d) for the given system.