Question

The temperature of an ideal gas in a sealed 0.40m3 rigid container is reduced from 350 K to 270 K.The final pressure of the gas is 60 kPa. The molar heat capacity at constant volume of the gas is 28.0 J/(mol K). The heat absorbed by the gas is closest to

Answer 1

Answer:

The answer is below

Explanation:

Given that the volume (V) = 0.4 m³, temperature difference (ΔT) = 270 K - 350 K = -80 K, pressure (P) = 60 kPa = 60000 Pa, R = 8.314 J/molK

Since we have constant volume, we can use the final state parameters to calculate the number of moles using the ideal gas law:

$PV=nRT\\\\n=\frac{PV}{RT} =\frac{60000*0.4}{8.314*270} =10.69\ moles$

Given that the molar heat capacity at constant volume ($C_v$) = 28.0 J/(mol K), the heat absorbed (Q) is:

$Q=nC_v\Delta T=10.69*28*(-80) = -23945.6\ J\\\\Q=-23.95\ kJ$

Q ≈ -24 kJ