One mole of an ideal monoatomic gas is caused to go through the cycle shown in figure. Then, the change in the internal energy is expanding the gas fr

Question

One mole of an ideal monoatomic gas is caused to go through the cycle shown in figure. Then, the change in the internal energy is expanding the gas fr

One mole of an ideal monoatomic gas is caused to go through the cycle shown in figure. Then, the change in the internal energy is expanding the gas from a to `c` along the path `abc` is:
A. `3P_(0)V_(0)`
B. `6 RT_(0)`
C. `4.5 RT_(0)`
D. `10.5 RT_(0)`

Monjur Alahi

7 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - D
`Pv= nRT` at point `C`
`2P_(0)xx4V_(0)=1xxRT_(c)`
`T_(c )=[(8P_(0)V_(0))/(R )]`
at point a
`P_(0)V_(0)=1xxRT_(0)`
`T_(0)=(P_(0)V_(0))/(R ) , T_(c )=8T_(0)`
change in internal energy `=[ nC_(v)dT]`
For path `a` to `b=1xx(3)/(2)Rxx[3T_(0))=(9)/(2)RT_(0)`
For path `b` to `c=1xx(3)/(2)Rxx[4T_(0)]=6T_(0)R`
Total change `=(9)/(2)RT_(0)+6RT_(0)=(21RT_(0))/(2)=10.5 RT_(0)`
So total change in internal energy
`Delta U =10.5 RT_(0)`