Question

A cylinder with a piston holds 3.50 moles of a diatomic gas. The gas in the cylinder absorbs 895 J of energy due to the higher temperature of the environment. At the same time, the cylinder expands to a larger volume, doing 152 J of work on the environment.

(b)
What is the change in temperature of the gas (in K)?

Answer 1

Explanation:

To determine the change in temperature of the gas, we can use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system:

ΔU = Q - W

In this case, the gas absorbs 895 J of energy (Q) and does 152 J of work (W) on the environment. Therefore:

ΔU = 895 J - 152 J

ΔU = 743 J

Now, we can relate the change in internal energy (ΔU) to the change in temperature (ΔT) using the specific heat capacity (C) and the number of moles (n) of the gas:

ΔU = nCΔT

Rearranging the equation to solve for ΔT:

ΔT = ΔU / (nC)

First, we need to determine the specific heat capacity of the diatomic gas. The specific heat capacity depends on the gas and its molecular structure. Assuming the gas behaves ideally and is diatomic, we can use the molar specific heat capacity at constant volume (Cv) for diatomic gases, which is approximately 20.8 J/(mol·K).

Substituting the known values into the equation:

ΔT = 743 J / (3.50 mol * 20.8 J/(mol·K))

Calculating:

ΔT ≈ 10.90 K

Therefore, the change in temperature of the gas is approximately 10.90 Kelvin (K).