Question

The equation of state of a gas is given as bar v(P+10/bar v^2) = RsubuT, where the units of bar v and P are m^3/kmol and kPa respectively. Now 0.49 kmol of this gas is expanded in a quasi-equilibrium manner from 1.6 to 4.9 m^3 at a constant temperature of 290 K. Determine the work done during this isothermal expansion process.

Answer #1

A 2.0 mol sample of ideal gas with molar specific heat
Cv = (5/2)R is initially at 300 K and 100 kPa pressure. Determine
the final temperature and the work done on the gas when 1.6 kJ of
heat is added to the gas during each of these separate processes
(all starting at same initial temperature and pressure: (a)
isothermal (constant temperature) process, (b) isometric (constant
volume) process, and (c) isobaric (constant pressure) process.
Hint: You’ll need the 1st Law...

The van der Waals equation of state is (P + a(n/V )^2)(V/n − b)
= RT, where a and b are gas-specific constants. For Hydrogen gas, a
= 2.45 × 10^-2P a · m^6 and b = 26.61 × 10^-6m^3/mol, while for an
ideal gas a = b = 0. (a) Consider trying to measure the ideal gas
constant in a lab from the relation R = P V/(nT), where P, V, n,
and T are all measured parameters. However,...

Ten liters of a monoatomic ideal gas at 25o C and 10
atm pressure are expanded to a final pressure of 1 atm. The molar
heat capacity of the gas at constant volume, Cv, is 3/2R and is
independent of temperature. Calculate the work done, the heat
absorbed, and the change in U and H for the gas if the process is
carried out
(1) isothermally and reversibly, and
(2) adiabatically and reversibly.
Having determined the final state of the...

A gas is represented by the equation of state P= RT( 1/V + A/V^2
+ B/V^3)
Express A and B in terms of critical constants. Hint: Use the
expressions for critical behavior.

When gas expands in a cylinder with radius r, the
pressure P at any given time is a function of the volume
V: P = P(V). The force exerted
by the gas on the piston (see the figure) is the product of the
pressure and the area: F =
πr2P. The work done by the
gas when the volume expands from volume V1 to
volume V2 is
W =
V2
P
dV
V1
.
In a steam engine the pressure...

Two moles of nitrogen are initially at 10 bar and 600 K (state
1) in a horizontal piston/cylinder device. They are expanded
adiabatically to 1 bar (state 2). They are then heated at constant
volume to 600 K (state 3). Finally, they are isothermally returned
to state 1. Assume that N 2 is an ideal gas with a constant heat
capacity as given on the back flap of the book. Neglect the heat
capacity of the piston/cylinder device. Suppose that...

As will be discussed in detail in Chapter 5, the
ideal-gas equation of state relates absolute pressure, P(atm); gas
volume, V(liters); number of moles of gas, n mol ; and absolute
temperature, T(K): PV 0:08206nT
(a) Convert the equation to one relating P psig , V
(ft3) , n (lb-mole) , and T (°F) .
(b) A 30.0 mole%CO and 70.0 mole%N2 gas mixture is
stored in a cylinder with a volume of 3.5ft^3 at a temperature of
85°F. The...

A 1.65 mol of an ideal gas (Cv=3R/2) at T=14.5 oC and P=0.2 bar
undergoes the following two step process: first an isothermal
expansion against a constant pressure of 0.1 bar until the volume
is doubled; followed by a cooling to -35.6 oC at constant volume.
Calculate the following thermodynamic quantities for the total
process:
1) Work (w) for step 1.
2) Heat (Q) for step 1.
3) Change in internal energy (U) for step 1.
4) Change in enthalpy...

6) A helium gas containing 10^26 He atoms has a pressure of 10.0 atm at a volume of 1.00 m^3.
a) What is its temperature?
b) If an isothermal process expands the gas to 3.00 m^3, what is then the pressure?
c) Would heat have to be added or removed in order to do this?
d) If the expansion was instead adiabatic, would the work needed be smaller or larger? why?
7) A 1.5 kg mass is hanging from a...

A 5 kg mass of R134a refrigerant is compressed
polytropically from the state initial: p1 = 1 bar, T1 = 27 ° C
until the final state: p2 = 15 bar, T2 = 227 ° C. Specific heat
R134a medium at constant volume, Cv = 0.72 kJ / kg K.
Calculate:
a) exponent of polytropy;
b) final volume;
c) final volume using the virial state equation d) work done on the
gas for compression;
e) amount of heat given up...

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