One mole of a monatomic ideal gas undergoes a | vedclass

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

Question

(C) For an adiabatic process,the relation between temperature and volume is $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$.For a monatomic gas,the adiabati

Vedclass · Accepted Answer

$900$

Vedclass · Answer

(C) For an adiabatic process,the relation between temperature and volume is $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$.For a monatomic gas,the adiabatic index $\gamma = \frac{5}{3}$,so $\gamma - 1 = \frac{2}{3}$.Given $V_2 = 8 V_1$ and $T_1 = 100 K$.$T_2 = T_1 \left(\frac{V_1}{V_2}ight)^{\gamma-1} = 100 	imes \left(\frac{1}{8}ight)^{2/3} = 100 	imes \left(\frac{1}{4}ight) = 25 K$.The change in internal energy is given by $\Delta U = n C_v \Delta T$.For a monatomic gas,$C_v = \frac{3}{2} R$.$\Delta U = 1 	imes \frac{3}{2} 	imes 8.0 	imes (25 - 100) = 12 	imes (-75) = -900 J$.The decrease in internal energy is $|\Delta U| = 900 J$.

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $100 K$ and the universal gas constant $R = 8.0 J mol^{-1} K^{-1}$,the decrease in its internal energy,in Joule,is. . . . .

Similar Questions

The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from $5 \ L$ to $4 \ L$. The ratio of initial pressure to final pressure is:

$A$ graph of pressure versus volume for an ideal gas for different processes is as shown. In the graph,curve $OC$ represents:

Two moles of a gas at a temperature of $327^{\circ} C$ expands adiabatically such that its volume increases by $700 \%$. If the ratio of the specific heat capacities of the gas is $\frac{4}{3}$, then the work done by the gas is (Universal gas constant $= 8.3 \ J \ mol^{-1} \ K^{-1}$) (in $kJ$)

$5$ moles of Hydrogen $\left(\gamma=\frac{7}{5}\right)$ initially at $S.T.P.$ are compressed adiabatically so that its temperature becomes $400^{\circ} C$. The increase in the internal energy of the gas in kilo-joules is $\left(R=8.30 \ J \ mol^{-1} \ K^{-1}\right)$.

For adiabatic processes $\left( \gamma = \frac{C_p}{C_v} \right)$,which of the following relations is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module