1 , text{mole} of an ideal monoatomic gas at | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For a monoatomic gas,the molar heat capacity $C$ for a process $P = KV$ is calculated as follows:Given $P = KV$,we know $PV = nRT$. Substituting $

Vedclass · Accepted Answer

$2RT_0$

Vedclass · Answer

(B) For a monoatomic gas,the molar heat capacity $C$ for a process $P = KV$ is calculated as follows:Given $P = KV$,we know $PV = nRT$. Substituting $P = KV$,we get $KV^2 = nRT$,so $V^2 \propto T$.For a polytropic process $PV^x = 	ext{constant}$,we have $T V^{x-1} = 	ext{constant}$.Since $V^2 \propto T$,we have $T V^{-2} = 	ext{constant}$,which implies $x - 1 = -2$,so $x = -1$.The molar heat capacity $C$ is given by $C = C_v + \frac{R}{1-x} = \frac{3}{2}R + \frac{R}{1-(-1)} = \frac{3}{2}R + \frac{R}{2} = 2R$.The heat supplied is $Q = nC\Delta T = 1 	imes (2R) 	imes (2T_0 - T_0) = 2RT_0$.

$1 \, \text{mole}$ of an ideal monoatomic gas at temperature $T_0$ expands slowly according to the law $P = KV$,where $K$ is a constant. If the final temperature of the gas is $2T_0$,find the heat supplied to the gas.

Similar Questions

An ideal gas expands in such a manner that its pressure and volume are related by the equation $PV^2 = \text{constant}$. During this process, the gas is

$A$ thermodynamic process for one mole of an ideal gas is shown below on a $P-V$ diagram. If $V_{2} = 2V_{1}$, then the ratio of temperature $T_{2} / T_{1}$ is ...... .

Hydrogen gas is undergoing a process given by $PV^2 = \text{constant}$. The ratio of work done by the gas to the change in its internal energy is

An ideal gas undergoes a polytropic process given by the equation $PV^n = \text{constant}$. If the molar heat capacity of the gas during this process is the arithmetic mean of its molar heat capacity at constant pressure $(C_P)$ and constant volume $(C_V)$, then the value of $n$ is ..............

$1 \, \text{mole}$ of an ideal gas at temperature $T_1$ expands according to the law $P/V = \text{constant}$. Find the work done when the final temperature becomes $T_2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module