The temperature of 6.80 mol of an ideal monatomic gas is raised 12.0 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 calculate the work done by the gas (W), energy transferred as heat (Q), change in internal energy (ΔEint), and change in average kinetic energy per atom (ΔK), we need to use the formulas and concepts related to thermodynamics. Here's how you can get the answers:
(a) The work done by the gas (W) can be calculated using the formula:
W = -nCvΔT
where n is the number of moles of the gas, Cv is the molar heat capacity at constant volume, and ΔT is the change in temperature.
Given:
n = 6.80 mol
ΔT = 12.0 K
To get the value of Cv, we need to know the specific heat capacity of the gas. For an ideal monatomic gas, the molar heat capacity at constant volume is:
Cv = (3/2)R
where R is the ideal gas constant (R = 8.31 J/(mol·K)).
Substituting the values, we have:
Cv = (3/2) * 8.31 J/(mol·K)
Now, plug in the values of n, Cv, and ΔT into the formula to calculate the work done by the gas (W).
(b) The energy transferred as heat (Q) can be calculated using the first law of thermodynamics:
ΔEint = Q - W
In an adiabatic process, Q = 0 since there is no heat transfer. Therefore, the energy transferred as heat (Q) is zero.
(c) The change in internal energy (ΔEint) of the gas can be calculated using the formula:
ΔEint = Q - W
Since we know Q = 0, the change in internal energy (ΔEint) is equal to the work done by the gas (W).
(d) To calculate the change in average kinetic energy per atom (ΔK), we can use the formula:
ΔK = (3/2)RΔT
where ΔT is the change in temperature.
Substituting the values of ΔT and R into the formula, we can calculate the change in average kinetic energy per atom (ΔK).
By following these steps, you can calculate the values of (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.