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 Δ T. The amount of heat absorbed by gas is (R is gas constant) :

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 Δ T. The amount of heat absorbed by gas is (R is gas constant) : (A) (1/2) R Δ T (B) (3/2) R Δ T (C) (1/2) K R Δ T (D) (2K/3) Δ T

Tardigrade Admin · Accepted Answer

VT =K ⇒ V((PV/nR)) =k ⇒ PV2 = K ∵ C = (R/1-x) +CV (For polytropic process) C = (R/1-2) + (3R/2) = (R/2) ∴ Δ Q = nC Δ T = (R/2) ×Δ T

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

$\frac{1}{2} R Δ T$

$\frac{3}{2} R Δ T$

$\frac{1}{2} K R Δ T$

$\frac{2 K}{3} Δ T$

$V T = K$
$\Rightarrow V (\frac{P V}{n R}) = k \Rightarrow P V^{2} = K$
$∵ C = \frac{R}{1 - x} + C_{V}$ (For polytropic process)
$C = \frac{R}{1 - 2} + \frac{3 R}{2} = \frac{R}{2}$
$∴ Δ Q = n C Δ T$
$= \frac{R}{2} \times Δ T$

Q. 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 ΔT. The amount of heat absorbed by gas is (R is gas constant) :

21​RΔT

23​RΔT

21​KRΔT

32K​ΔT