Question

In a thermodynamic process, temperature and volume of one mole of an ideal monatomic gas are varied according to the relation $VT=k$ , where $k$ is a positive constant. In this process, if the temperature of the gas increases by $\Delta T$ , then the amount of heat absorbed by gas is [ $R$ is the universal gas constant]

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

Answer 1

Answer: (A)

$VT=K$
From ideal gas equation $pv=nRT$
$P{V}^2=$ Constant
For polytrophic $=w=\frac{P_1{V}_1-P_2{V}_2}{x-1}=nR\frac{\left(T_1-T_2\right)}{x-1}=\frac{-nR\Delta T}{2-1}=-nR\Delta T$
$Q=\Delta u+w$
$Q=\frac{3}{2}R\Delta T-nR\Delta T=\frac{1}{2}R\Delta TQ=\frac{3}{2}R\Delta T-nR\Delta T=\frac{1}{2}R\Delta T$