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

The answer is below

Step-by-step 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=(PV)/(RT) =(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