If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic

Question

If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is [2026]

Smart Achievers · Accepted Answer

(4)

$T_{mix} = \frac{n_{1} C_{1} T_{1} + n_{2} C_{2} T_{2}}{n_{1} C_{1} + n_{2} C_{2}}$

$= \frac{(2 \times \frac{3}{2} R \times T) + (6 \times \frac{3}{2} R \times 2 T)}{(2 \times \frac{3}{2} R) + (6 \times \frac{3}{2} R)}$

$T_{mix} = \frac{2 T + 12 T}{8} = \frac{7}{4} T$

Solution

Q.
If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is [2026]

1 $\frac{5}{2} T$

2 $\frac{5}{4} T$

3 $\frac{7}{2} T$

4 $\frac{7}{4} T$

Ans.
(4)

$T_{mix} = \frac{n_{1} C_{1} T_{1} + n_{2} C_{2} T_{2}}{n_{1} C_{1} + n_{2} C_{2}}$

$= \frac{(2 \times \frac{3}{2} R \times T) + (6 \times \frac{3}{2} R \times 2 T)}{(2 \times \frac{3}{2} R) + (6 \times \frac{3}{2} R)}$

$T_{mix} = \frac{2 T + 12 T}{8} = \frac{7}{4} T$

Want Us to Email you About Special Offers & Updates?

Solution

Q. If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is [2026]

1 52T

2 54T

3 72T

4 74T

Ans. (4) Tmix=n1C1T1+n2C2T2n1C1+n2C2 =(2×32R×T)+(6×32R×2T)(2×32R)+(6×32R) Tmix=2T+12T8=74T