Use the ideal gas law to complete the table:
P
V
n
T
1.06 atm
1.25 L
0.105 mol
___
115 torr
___
0.249 mol
309 K
___
28.2 mL
1.81×10−3 mol
26.0 ∘C
0.565 atm
0.440 L
___
257 K
For an ideal gas, consider the molar volume Vm = (V/n) =
Vm(T,P). In other words, the molar volume is a function of
temperature and pressure.
a) Write the total differential dVm.
b) Show that dVm is exact.
c) Derive an expression for the differential work dw performed
in a reversible process by expansion/compression of the gas.
d) Show that dw is inexact.
e) What is the thermodynamic significance of having an exact
differential?
Three moles of an ideal monatomic gas expand at a constant
pressure of 2.10 atm ; the volume of the gas changes from 3.30×10−2
m3 to 4.50×10−2 m3 .
a) Calculate the initial temperature of the gas.
b) Calculate the final temperature of the gas.
c) Calculate the amount of work the gas does in expanding.
d) Calculate the amount of heat added to the gas.
e) Calculate the change in internal energy of the gas
Suppose 1.0 mol of an ideal gas is initially at P=4.0
atm and T=400 K. It is expanded irreversibly and adiabatically
against a constant pressure of 1.0 atm until the volume has
doubled.
(a) Calculate the final volume of the gas.
(b) Calculate w, q, and energy change ΔU of this process, in
joules.
(c) Calculate the final temperature of the gas.
(d) Calculate the entropy change ΔS of the ideal gas in the
process.
(e) What is the entropy...
For 1 mol of an ideal gas, Pexternal = P = 1 atm. The
temperature is changed from 125ºC to 25.0ºC, and CV,m = 3/2R.
Calculate (all units are J) q= , w= , ∆U= , and ∆H= . Please enter
your answers with 2 decimals in E notation, such as 2.33E4
(=23345). If the answer is negative, please do not forget the
negative sign. If answer is zero, please just enter 0 without
decimal.
A quantity of N molecules of an ideal gas initially occupies
volume V. The gas then expands to volume 2V. The number of
microscopic states of the gas increases in the expansion. Under
which of the following circumstances will this number increases the
most? ( i ) if the expansion is reversible and isothermal ( ii ) if
the expansion is reversible and adiabatic ( iii ) the number will
change by the same amount for both circumstances. Why ?
The ideal gas law PV=nRT relates pressure P, volume V,
temperature T, and number of moles of a gas, n. The gas constant R
equals 0.08206 L⋅atm/(K⋅mol) or 8.3145 J/(K⋅mol). The equation can
be rearranged as follows to solve for n: n=PVRT This equation is
useful when dealing with gaseous reactions because stoichiometric
calculations involve mole ratios.
Part A
When heated, calcium carbonate decomposes to yield calcium oxide
and carbon dioxide gas via the reaction CaCO3(s)→CaO(s)+CO2(g) What
is the mass...
The ideal gas law can be stated as P V = nRT where P = pressure
in Pascals (Pa) V = volume in cubic meters (m3 ) n = number of
moles in moles (mol) R = gas constant = 8.3145m3 Pa / ( K · mol ) T
= temperature in Kelvin (K). Using MATLAB or Octave, Write a script
that prompts the user for the pressure, the volume, and the
temperature; storing each in a variable. The script...
One mole of an ideal gas in an initial state P = 10atm, V = 5L,
is taken reversibly in aclockwise direction around a circular path
given by (V − 10)^2 + (P − 10)^2 = 25. Computethe amount of work
done by the gas and the change in internal energy.