Two containers, X and Y, both contain nitrogen gas at a temperature of 30° C and

Question

Two containers, X and Y, both contain nitrogen gas at a temperature of 30° C and a pressure of 1 atm. The initial volume of each of the containers is V30 = 0.5 liters. The only difference between the two containers is that while container X has a piston that is sealed and cannot move, the gas in container Y is allowed to expand against the surrounding atmosphere.

QX is the amount of heat required to raise the temperature of the gas in container X by 10° C, and QY is the amount of heat required to raise the temperature of the gas in container Y by 10° C.

What is the difference between QX and QY?

Use 0°C = 273.15 K

QX - QY =

Explanation / Answer

the container X undergoes constant volume process hence the heat energy required Qx=ncvdT

the container Y undergoes constant constant pressure process so QY=ncpdT

QX-QY= ncvdT-ncpdT=-nRdT = -p0v0 /RT0  (RdT)= -1.0(10)5(0.5)(10)-3(10) /303.15) =-1.649J=-1.65J

here P0=1atm=1.01(10)5 pas and V0=0.5(10)-3m3   T0=30+273.15=303.15 n=number of moles dT=10

cv,cp =molar specific heats at constant volume and constant pressure

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