One mole of an ideal gas with gamma = 1.4 is | vedclass

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

Question

(B) The change in internal energy $\Delta U$ of an ideal gas is given by the formula $\Delta U = n C_v \Delta T$.For an ideal gas,$C_v = \frac{R}{\gam

Vedclass · Accepted Answer

$166$

Vedclass · Answer

(B) The change in internal energy $\Delta U$ of an ideal gas is given by the formula $\Delta U = n C_v \Delta T$.For an ideal gas,$C_v = \frac{R}{\gamma - 1}$.Given: $n = 1 \, mol$,$\gamma = 1.4$,$R = 8.3 \, J/mol \cdot K$.Initial temperature $T_1 = 27^{\circ}C = 27 + 273 = 300 \, K$.Final temperature $T_2 = 35^{\circ}C = 35 + 273 = 308 \, K$.Change in temperature $\Delta T = T_2 - T_1 = 308 - 300 = 8 \, K$.Substituting the values:$\Delta U = 1 	imes \frac{8.3}{1.4 - 1} 	imes 8$$\Delta U = \frac{8.3}{0.4} 	imes 8$$\Delta U = 8.3 	imes 20 = 166 \, J$.Thus,the change in internal energy is $166 \, J$.

One mole of an ideal gas with $\gamma = 1.4$ 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 ....... $J$ $(R = 8.3 \, J/mol \cdot K)$.

Similar Questions

Assertion $(A)$: When an ideal gas is compressed adiabatically,its temperature and the average kinetic energy of the gas molecules increase.
Reason $(R)$: The kinetic energy increases because of collisions of molecules with the moving parts of the wall.

During adiabatic expansion,if the temperature of $3$ moles of a diatomic gas decreases by $50^{\circ} C$,then the work done by the gas is (where $R$ is the Universal gas constant). (in $R$)

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

$P-V$ plots for two gases during adiabatic processes are shown in the figure. Plots $1$ and $2$ should correspond respectively to

An ideal gas at $27^{\circ} C$ is compressed adiabatically to $8/27$ of its original volume. If $\gamma = 5/3$,the rise in temperature of the gas is: (in $K$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module