Two moles of an ideal monoatomic gas occupy a | vedclass

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

Question

(B) For an adiabatic process,the relation between temperature and volume is $T_1 V_1^{\gamma - 1} = T_2 V_2^{\gamma - 1}$.Given: $n = 2 \ mol$,$T_1 =

Vedclass · Accepted Answer

$(a) 189 \ K, (b) -2.7 \ kJ$

Vedclass · Answer

(B) For an adiabatic process,the relation between temperature and volume is $T_1 V_1^{\gamma - 1} = T_2 V_2^{\gamma - 1}$.Given: $n = 2 \ mol$,$T_1 = 27^{\circ}C = 300 \ K$,$V_1 = V$,$V_2 = 2V$.For a monoatomic gas,the adiabatic index $\gamma = 5/3$,so $\gamma - 1 = 2/3$.$(a)$ Substituting the values: $300 	imes V^{2/3} = T_2 	imes (2V)^{2/3}$.$T_2 = 300 / (2^{2/3}) \approx 300 / 1.5874 \approx 189 \ K$.$(b)$ The change in internal energy is given by $\Delta U = n C_v \Delta T$.For a monoatomic gas,$C_v = (3/2)R$.$\Delta U = 2 	imes (3/2) 	imes 8.314 	imes (189 - 300) \approx 3 	imes 8.314 	imes (-111) \approx -2768 \ J \approx -2.7 \ kJ$.

Two moles of an ideal monoatomic gas occupy a volume $V$ at $27^{\circ}C$. The gas expands adiabatically to a volume $2V$. Calculate $(a)$ the final temperature of the gas and $(b)$ the change in its internal energy.

Similar Questions

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in the $P-V$ diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is:

One mole of an ideal gas at an initial temperature of $T \, K$ does $6 \, R \, \text{joules}$ of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $\frac{5}{3}$, the final temperature of the gas will be

You feel refreshed by taking a shower in summer but not in winter. Why?

One mole of an ideal gas $\left(\gamma = \frac{5}{3}\right)$ at $127^{\circ} C$ is compressed adiabatically to $\left(\frac{8}{27}\right)$ of its initial volume. Find the magnitude of the work done on the system in $cal$.

One mole of an ideal gas $(\gamma = 1.4)$ is adiabatically compressed so that its temperature rises from $27\,^{\circ}C$ to $35\,^{\circ}C$. The change in the internal energy of the gas is .... $J$ (given $R = 8.3 \,J/mol/K$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module