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 increased 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. $\frac{1}{2}KR\Delta T$
• D. $\frac{2K}{3}\Delta T$

Answer 1

Answer: (A)

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

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