By First law of thermodynamics we have
#Q=dU+W.....[1]#
Where
#Q-> "heat given to the system" =nC_pdT#
#dU-> "change in internal energy of the system" =nC_vdT#
#W-> "work done by the system" #
Here #n-> "number of mole of the gas"#
#C_p->" molar heat capacity of the gas at constant pressure"#
#C_v->" molar heat capacity of the gas at constant volume"#
#dT-> "change in temprature"#
So equation [1] becomes
#nC_pdT=nC_vdT+W#
#=>W=n(C_p-C_v)dT=nRdT#
Inserting
# n=1mol#
# R =0.082LatmK^-1mol^-1=0.0082kJK^-1mol^-1 #
(as 1Latm =-.1kJ)
#dT=(273-373)K=-100K#
So work done by the system
#=>W=nRdT=1molxx0.0082kJK^-1mol^-1xx(-100K)#
#=-0.82kJ#
Here work done by the system is negative . So this means that work is to be done on the system for the cooling process as the process is not adiabatic one and the amount of work done on the system will be #0.82kJ#
