Question

A cylinder with a piston holds 4.00 moles of a diatomic gas. The gas in the cylinder absorbs 955 J of energy due to the higher temperature of the environment. At the same time, the cylinder expands to a larger volume, doing 132 J of work on the environment. Answer parts a-b.

Answer 1

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.