Given :
Heat absorbs , Q = 10 J .
Pressure , [tex]P=0.5 \ atm =0.5\times 101325\ Pa[/tex]
Initial volume , [tex]V_i=4\ L[/tex] .
Final volume , [tex]V_f=2\ L[/tex] .
To Find :
The change in the internal energy .
Solution :
By first law of thermodynamics :
[tex]\Delta U=Q+W[/tex]
Here , W is work done , [tex]W=-P\Delta V=-P\times (V_f-V_i)[/tex]
Therefore,
[tex]\Delta U=Q-P(V_f-V_i)[/tex]
Putting values in SI units in above equation :
[tex]\Delta U=10 -(0.5\times 101325\times (2-4)\times 10^{-3})\\\\\Delta U=111\ J[/tex]
Therefore , option b. is correct .
Hence , this is the required solution .
