Four moles of a diatomic gas (g = 1.4) at a temperature of 300 K were cooled isochorically, so that the final pressure was 1/3 times the original pressure. The gas was allowed to expand isobarically till its temperature got back to its original value. Calculate the total amount of heat absorbed during the process. R = 8.31 J mol ^(-1) K ^(-1).

Four moles of a diatomic gas (g = 1.4) at a temperature of 300 K were

1.	Four moles of a diatomic gas (g = 1.4) at a temperature of 300 K were cooled isochorically, so that the final pressure was 1/3 times the original pressure. The gas was allowed to expand isobarically till its temperature got back to its original value. Calculate the total amount of heat absorbed during the process. R = 8.31 J mol ^(-1) K ^(-1).
Answer» Solution :NUMBE of MOLES `n = 4` `gamma = 1.4` Initial temperature `T_(1) = 300 K` At the end of the isochoric process the pressure becomes three times the initial pressure. So the temperature becomes `(T_(1))/( 3).` Heat absorbed during the process is `Q_(1).` `Q_(1) = Delta U _(1)+ P Deltaa V, Delta V =0` for an isochoric process. `Q _(1) = (n RT Delta T)/( gamma -1) = ( n R)/( gamma -1) ((T_(1))/( 3) - T_(1))` `= ( n RT_(1))/( gamma -1)((1-3)/(3))` `= ( 4 xx 8.31 xx 300 xx ((-2)/(3)))/(1.4 - 1) = - 16620J`