Three moles of an ideal monatomic gas expands at a constant pressure of 2.5atm ; the volume of the gas changes from 3.2×10-2m3to 4.5×10-2m3. Calculate (a) the initial and final temperatures of the gas; (b) the amount of work the gas does in expanding; (c) the amount of heat added to the gas; (d) the change in internal energy of the gas.

Short Answer

Expert verified

a.T1=325KT2=457Kb.W=3293Jc.Q=8231JΔd.U=4938J

Step by step solution

01

The equations involved

The ideal gas equation is pV = nRT.

Work done at constant pressure is given byW=pV.

The heat energy is given byQ=nCPΔT.

First law of thermodynamics isQ=W+ΔU.

02

Use ideal gas equation to find the temperatures

T1=pV1nRT1=2.5×101325×3.2×10-23×8.314T1=325KT2=pV2nRT2=2.5×101325×4.5×10-23×8.314T2=457K

03

Calculate the work done

W=p(V2-V1)W=2.5×101325×(0.045-0.032)W=3293J

04

Calculate the heat energy involved

Q=nCPΔTQ=n×2.5RΔTQ=3×2.5×8.314×(457-325)Q=8231J

05

Calculate the internal energy

Q=W+ΔUΔU=Q-WΔU=8231-3293ΔU=4938J

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