Question

If you supply 2300 j of heat to 6.00 moles of an ideal diatomic gas initially at 21.0 ∘c in a perfectly rigid container, what will be the final temperature of the gas?

Answer 1

To find the final temperature of the gas, we can use the equation Q = nCΔT, where Q is the heat supplied to the gas, n is the number of moles, C is the molar heat capacity of the gas, and ΔT is the temperature change. Substituting the given values, the final temperature is approximately 39.03 °C.

Step-by-step explanation:

To find the final temperature of the gas, we can use the equation:

Q = nCΔT

where Q is the heat supplied to the gas, n is the number of moles of gas, C is the molar heat capacity of the gas, and ΔT is the temperature change.

In this case, the heat supplied to the gas is 2300 J and the number of moles is 6.00. The molar heat capacity for a diatomic gas at constant volume is approximately 20.8 J/(mol⋅K). We can rearrange the equation to solve for the temperature change:

ΔT = Q / (nC)

Substituting the given values:

ΔT = 2300 J / (6.00 mol * 20.8 J/(mol⋅K))

ΔT ≈ 18.03 K

Lastly, to find the final temperature, we add the change in temperature to the initial temperature:

Final temperature = 21.0 °C + 18.03 K = 39.03 °C