find the amount of work done to increase temperature of 1mole of an ideal gas by 30 c if it - Physics - Thermodynamics

Question

find the amount of work done to increase temperature of 1mole of an
ideal gas by 30 c if it is expanding under condition v directly
proportional to t^2/3 Given R=1 99cal mol/k and 1cal=4 2j

Vara · Accepted Answer

Dear
Student,
Please find below the solution
to the asked query:
From Ideal gas equation:PV=RT=RTVGiven condition:V α T2/3V = K T2/3dVdT=23KT-13dV=23KT-13 dTWork done:W=∫PdV=∫RTV23KT-13 dT=∫RTK T2/323KT-13 dT=23∫RdT=2R3TTT+∆T=2R3∆T=2×1
993×30=39 8 cal=39 8 ×4
2 J=167 J
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find the amount of work done to increase temperature of 1mole of an ideal gas by 30 c if it is expanding under condition v directly proportional to t^2/3.Given R=1.99cal mol/k and 1cal=4.2j.