Question

An expandable cube, initially 23 cm on each side contains 2.6 g of helium at 20∘C. 1000 J of heat energy are transferred to this gas.

What is the final pressure if the process is at constant volume?

What is the final volume if the process is at constant pressure?

Answer 1

initial volume of helium

V1=(0.23m)³=0.01217m³=12.17L

initial pressure of helium

P1=nRT1/V1.......................eqn 1

n=m/M=2.6g/4.003g per mole=0.6495 g moles

so putting the values of eqn 1

P1=(0.6495g mol *0.08206 Latm mol^-1*293.15k)/12.17L

P1 =1.284 atm

for constant volume

T2=T1+(Q/m Cv)

T2=20C+(1000J)/2.6g*3.1156J/g-C)

=416.6 K

P2=P1* (T2/T1)=1.284*(416.6/293.15)=1.825 atm

P2=1.825 atm

for constant pressure

T2=T1+(Q/m*cp)

=20C+(1000J/2.6g*5.1296J/g-C

T2=368.13 K

V2=V1* (T2/T1)

V2=12.17L (368.13/293.15)=15.33 L

so answer is 1.825 atm and 15.33 L