Question

Six grams of hydrogen gas at a temperature of 273 K isothoermally expanded to five times its initial volume and then isochorically heated so that the pressure in the final state becomes equal to that in the initial state. Find the total amount of heat absorbed by the gas during the entire process.

Answer 1

The processes represent on the P-V diagram by the curve 1 to 2 (isothermal) and the line 2 to 3 (isochoric), Here
`P_(1) = P_(3)`
For the process 1 to 2 (isothermal)
`T_(2) = T_(1), V_(2) = 5 V_(1)`
`Delta H = Delta U + W = 0 + W`
`implies Delta H = 2.303 nRT_(1) log ((V_(2))/(V_(1)))`
`Delta H = 2.303 xx ((6)/(2)) xx 8.3 xx 273 xx log 5 = 10942.4 J`
State 1 and state 3 are at the same pressure.
`implies (V_(1))/(T_(1)) = (V_(3))/(T_(3)) implies T_(3) = (V_(3))/(V_(1)) T_(1) = 5 xx 273 = 1365 K`
Process 2 to 3 : `Delta H = DeltaU + W`
`implies Delta H = nC_(V) Delta T + 0`
`DeltaH = (6)/(2) xx (5)/(2) R xx (T_(3) - T_(2))`
`implies Delta H = 7.5 xx 8.3 xx (1365 - 273) J = 67977 J`
Thus total heat absorbed `= Delta H_(1rarr 2) + Delta H_(2 rarr 3) = 78919.4 J`