The temperature of 4.60 mol of an ideal monatomic gas is raised 15.0 K in an adiabatic process. What are (a) the work W done by the gas, (b) the energy transferred as heat Q, (c) the change ΔEint in internal energy of the gas, and (d) the change ΔK in the average kinetic energy per atom?
To find the values of (a) the work done by the gas, (b) the energy transferred as heat, (c) the change in internal energy, and (d) the change in average kinetic energy per atom, we can use the following equations:
(a) The work done by the gas can be calculated using the equation:
W = -ΔEint
Here, ΔEint is the change in internal energy of the gas.
(b) The energy transferred as heat can be calculated using the first law of thermodynamics:
Q = ΔEint + W
(c) The change in internal energy of the gas can be calculated using the equation:
ΔEint = (3/2) nR ΔT
Here, n is the number of moles of the gas, R is the ideal gas constant, and ΔT is the change in temperature.
(d) The change in average kinetic energy per atom can be calculated using the equation:
ΔK = (3/2) R ΔT
Here, R is the ideal gas constant, and ΔT is the change in temperature.
Now let's plug in the given values to find the answers:
Given:
n = 4.60 mol
ΔT = 15.0 K
(a) To find the work done by the gas, we use the equation W = -ΔEint:
W = -[(3/2) nR ΔT]
= -[(3/2) (4.60 mol) (8.314 J/mol*K) (15.0 K)]
= -[(3/2) (4.60) (8.314) (15.0)]
(b) To find the energy transferred as heat, we use the equation Q = ΔEint + W:
Q = ΔEint + W
(c) To find the change in internal energy, we use the equation ΔEint = (3/2) nR ΔT:
ΔEint = (3/2) (4.60 mol) (8.314 J/mol*K) (15.0 K)
(d) To find the change in average kinetic energy per atom, we use the equation ΔK = (3/2) R ΔT:
ΔK = (3/2) (8.314 J/mol*K) (15.0 K)
By plugging in the given values into the respective equations, you will be able to find the values of (a) the work done, (b) the energy transferred as heat, (c) the change in internal energy, and (d) the change in average kinetic energy per atom.