Question

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $VT = K$, where $K$ is a constant. In this process the temperature of the gas is incresed by $\Delta T$. The amount of heat absorbed by gas is (R is gas constant) :

• A. $\frac{1}{2} R \Delta T$
• B. $\frac{3}{2} R \Delta T$
• C. $\frac{1}{2} K R \Delta T$
• D. $\frac{2K}{3} \Delta T$

Answer 1

Answer: (A)

$\frac{1}{2} R \Delta T$

Answer 2

$VT =K$
$\Rightarrow V\left(\frac{PV}{nR}\right) =k \Rightarrow PV^{2} = K$
$\because C = \frac{R}{1-x} +C_{V}$ (For polytropic process)
$C = \frac{R}{1-2} + \frac{3R}{2} = \frac{R}{2}$
$\therefore \Delta Q = nC \Delta T$
$= \frac{R}{2} \times\Delta T$