Question

One mole of an ideal monoatomic gas at temperature `T_0` expands slowly according to the law `p/V` = constant. If the final temperature is `2T_0`, heat supplied to the gas is
A. `2RT_(0)`
B. `RT_(o)`
C. `3/2RT_(0)`
D. `1/2RT_(0)`

Answer 1

Correct Answer - A
In a process `PV^(x)=` constant, molar heat capacity is given by `C=(R)/(gamma-1)+(R)/(1-x)`
As the process is `P/V`= constant,
i.e., `PV^(-1)=` constant, therefore, x= -1.
For an ideal monatomic gas, `gamma=5/3`
`thereforeC=(R)/(5/3-1)+(R)/(1-(-1))=3/2+R/2=2R`
`DeltaQ=nC(DeltaT)=1(2R)(2T_(0)-T_(0))=2RT_(0).`