3, text{moles} of an ideal gas at a temperatu | vedclass

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

Question

(B) The internal energy of an ideal gas is given by $U = n \left( \frac{f}{2} RT \right)$. Assuming both gases are monatomic $(f=3)$, the total energy

Vedclass · Accepted Answer

$107$

Vedclass · Answer

(B) The internal energy of an ideal gas is given by $U = n \left( \frac{f}{2} RT ight)$. Assuming both gases are monatomic $(f=3)$, the total energy is conserved.Energy of the first gas at $T_1 = 27^{\circ}\, 	ext{C} = 300\, 	ext{K}$ is $E_1 = 3 \left( \frac{3}{2} R 	imes 300 ight) = 1350\, R$.Energy of the second gas at $T_2 = 227^{\circ}\, 	ext{C} = 500\, 	ext{K}$ is $E_2 = 2 \left( \frac{3}{2} R 	imes 500 ight) = 1500\, R$.Let $T$ be the equilibrium temperature in Kelvin. The total energy of the mixture is $E_m = (3+2) \left( \frac{3}{2} RT ight) = 7.5\, RT$.By conservation of energy, $E_m = E_1 + E_2$.$7.5\, RT = 1350\, R + 1500\, R$.$7.5\, T = 2850$.$T = \frac{2850}{7.5} = 380\, 	ext{K}$.Converting to Celsius: $T(^{\circ}\, 	ext{C}) = 380 - 273 = 107^{\circ}\, 	ext{C}$.

$3\, \text{moles}$ of an ideal gas at a temperature of $27^{\circ}\, \text{C}$ are mixed with $2\, \text{moles}$ of an ideal gas at a temperature of $227^{\circ}\, \text{C}$. Determine the equilibrium temperature $(^{\circ}\, \text{C})$ of the mixture, assuming no loss of energy.

Similar Questions

$A$ gas mixture consists of $2.0$ moles of oxygen and $4.0$ moles of neon at temperature $T$. Neglecting all vibrational modes, calculate the total internal energy of the system. (Oxygen has two rotational modes.) (in $RT$)

If a mixture of $28 \, g$ of Nitrogen $(N_2)$,$4 \, g$ of Hydrogen $(H_2)$,and $8 \, g$ of Helium $(He)$ is contained in a vessel at temperature $400 \, K$ and pressure $8.3 \times 10^5 \, Pa$,the density of the mixture will be:

Two gases $A$ and $B$ having same pressure $P$,volume $V$,and absolute temperature $T$ are mixed. If the mixture has the volume and temperature as $V$ and $T$ respectively,then the pressure of the mixture is

$A$ vessel of volume $V$ contains a mixture of ideal gases at temperature $T$. The gas mixture contains $n_1, n_2$ and $n_3$ moles of three gases. Assuming an ideal gas system, the pressure of the mixture is

$A$ gaseous mixture contains $7 \ g$ of nitrogen and $20 \ g$ of argon. Assuming the gases are ideal,what are the specific heats $C_P$ and $C_V$ (in $J/g \ K$) for the mixture?

Vedclass Test Series

Exam Paper Generator

Online Exam Module