Answer:
a.Substituting the given values:
ΔU = 955 J - 132 J
ΔU = 823 J
Therefore, the change in internal energy of the gas in the cylinder is 823 J.
b. ΔT ≈ 49.78 K
Therefore, the change in temperature of the gas in the cylinder is approximately 49.78 K.
Step-by-step explanation:
To determine the change in internal energy of the gas in the cylinder, we need to consider the energy absorbed and the work done.
Given:
Number of moles of gas (n) = 4.00 moles
Energy absorbed (Q) = 955 J
Work done (W) = 132 J
a. Change in internal energy (ΔU):
According to the first law of thermodynamics, the change in internal energy (ΔU) of a system is given by the equation:
ΔU = Q - W
Substituting the given values:
ΔU = 955 J - 132 J
ΔU = 823 J
Therefore, the change in internal energy of the gas in the cylinder is 823 J.
b. Change in temperature (ΔT):
The change in internal energy (ΔU) of an ideal diatomic gas is related to the change in temperature (ΔT) using the equation:
ΔU = (n * Cv * ΔT)
where Cv is the molar specific heat capacity at constant volume.
Rearranging the equation, we can solve for ΔT:
ΔT = ΔU / (n * Cv)
The molar specific heat capacity at constant volume for a diatomic gas is approximately 5/2 R, where R is the gas constant.
Plugging in the values:
ΔT = 823 J / (4.00 mol * (5/2) R)
Note: The gas constant R has a value of approximately 8.314 J/(mol·K).
ΔT = 823 J / (4.00 mol * (5/2) * 8.314 J/(mol·K))
Calculating the value:
ΔT ≈ 49.78 K
Therefore, the change in temperature of the gas in the cylinder is approximately 49.78 K.