The temperature of 7.10 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 ÄEint in internal energy of the gas, and (d) the change ÄK in the average kinetic energy per atom?
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can u tell me how to calculate kinetic energy? formula is 3RT/2(avogadro no.)=3kT/2. BUT to calculate per atom instead of avogadro no I should place 1?
To find the values of work (W), heat transferred (Q), change in internal energy (ΔEint), and change in average kinetic energy per atom (ΔK), we need to use the following equations and principles:
(a) The work done by the gas (W) in an adiabatic process can be calculated using the equation:
W = -ΔEint
where W is the work done and ΔEint is the change in internal energy.
(b) In an adiabatic process, no heat is transferred (Q = 0). This is because adiabatic processes occur without any heat exchange with the surroundings.
(c) The change in the internal energy of the gas (ΔEint) can be calculated using the equation:
ΔEint = (3/2)nRΔT
where n is the number of moles, R is the ideal gas constant, and ΔT is the change in temperature.
(d) The change in the average kinetic energy per atom (ΔK) can be calculated using the equation:
ΔK = (1/2)m(Δv)^2
where m is the mass of an atom and Δv is the change in velocity.
Let's calculate each of these values step by step:
(a) Work done by the gas (W):
Since work (W) is equal to the negative change in internal energy (ΔEint), we can use the equation:
W = -(3/2)nRΔT
Substitute the given values:
n = 7.10 mol
R = Ideal gas constant = 8.314 J/mol·K
ΔT = 15.0 K
W = -(3/2)(7.10)(8.314)(15.0)
Calculate the value.
(b) Heat transferred (Q):
In an adiabatic process, no heat is transferred (Q = 0). Hence, Q = 0.
(c) Change in internal energy (ΔEint):
We can use the equation:
ΔEint = (3/2)nRΔT
Substitute the given values:
n = 7.10 mol
R = 8.314 J/mol·K
ΔT = 15.0 K
ΔEint = (3/2)(7.10)(8.314)(15.0)
Calculate the value.
(d) Change in average kinetic energy per atom (ΔK):
To calculate the change in average kinetic energy per atom, we need additional information such as the mass of the atoms and the change in velocity, which is not provided in the question. Without this information, we can't determine the change in average kinetic energy per atom (ΔK).
In summary:
(a) Calculate W using the equation W = -(3/2)nRΔT.
(b) Q = 0 since it is an adiabatic process.
(c) Calculate ΔEint using the equation ΔEint = (3/2)nRΔT.
(d) ΔK cannot be calculated without the mass and change in velocity information.