A tank contains 135 moles of the monatomic gas argon at a temperature of 15.3 °C. How much energy must be added to the gas to increase its temperature to 45.0 °C?

Question

Quizplus · Accepted Answer

The amount of energy needed to increase the temperature of a gas can be calculated using the formula:

ΔE = nCΔT

where:
ΔE = change in energy
n = number of moles of gas
C = molar specific heat capacity
ΔT = change in temperature

Since argon is a monatomic gas, its molar specific heat capacity at constant volume can be approximated as:
C = (3/2)R

where R is the universal gas constant.

Substituting the given values:

n = 135 mol
C = (3/2)R = (3/2)(8.31 J/mol·K) = 12.47 J/mol·K
ΔT = (45.0 - 15.3) °C = 29.7 °C = 29.7 K

ΔE = (135 mol)(12.47 J/mol·K)(29.7 K) = 4.99 × 10^4 J ≈ 5.00 × 10^4 J

Therefore, the best choice is C, 5.00 × 10^14 J.

A Tank Contains 135 Moles of the Monatomic Gas Argon